Show that vector A = (i - j)/√2 is a unit vector.

Show that vector A = (i - j)/√2 is a unit vector.
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Show that \(\vec{A} = \frac{\hat{i} - \hat{j}}{\sqrt{2}}\) is a unit vector. vector A = (i - j)/√2
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The expression 1/√2 (i + j) is a  (A) unit vector  (B) null vector  (C) vector of magnitude  (D) scalar

Description : The expression 1/√2 (i + j) is a  (A) unit vector  (B) null vector  (C) vector of magnitude  (D) scalar

Last Answer : The expression 1/√2 (i + j) is a (A) unit vector (B) null vector (C) vector of magnitude √2 (D) scalar

A fluid element has a velocity V = -y 2 . xi + 2yx 2 . j. The motion at (x, y) = (1/√2, 1) is (A) Rotational and incompressible (B) Rotational and compressible (C) Irrotational and compressible (D) Irrotational and incompressible

Description : A fluid element has a velocity V = -y 2 . xi + 2yx 2 . j. The motion at (x, y) = (1/√2, 1) is (A) Rotational and incompressible (B) Rotational and compressible (C) Irrotational and compressible (D) Irrotational and incompressible

Last Answer : (B) Rotational and compressible

P = i + 2k and Q = 2i + j -2k are two vectors, find the unit vector parallel to P x Q.

Description : P = i + 2k and Q = 2i + j -2k are two vectors, find the unit vector parallel to P x Q.

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i and j are unit vectors along X-axis and Y-axis respectively. What is the magnitude and direction of the vector i + j and i - j?

Description : i and j are unit vectors along X-axis and Y-axis respectively. What is the magnitude and direction of the vector i + j and i - j?

Last Answer : i and j are unit vectors along X-axis and Y-axis respectively. What is the magnitude and direction of the ... directions of (i + j) and (i - j)?

The unit vector to the points p1(0,1,0), p2(1,0,1), p3(0,0,1) is a) (-j – k)/1.414 b) (-i – k)/1.414 c) (-i – j)/1.414 d) (-i – j – k)/1.414

Description : The unit vector to the points p1(0,1,0), p2(1,0,1), p3(0,0,1) is a) (-j – k)/1.414 b) (-i – k)/1.414 c) (-i – j)/1.414 d) (-i – j – k)/1.414

Last Answer : a) (-j – k)/1.414

Find the tangent vector of line having end points P1(3,5,8) and P2 (6,4,3) a.3i+j-5k b.3i-j-5k c.3i-j+5k d.-3i-j-5k

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Last Answer : b.3i-j-5k

Complete the table vector given below: i, j, k

Description : Complete the table vector given below: i, j, k

Last Answer : Complete the table vector given below: \(\hat{i}\) \(\hat{j}\) \(\hat{k}\) \(\hat{i}\) - - - \(\hat{j}\) - - - \(\hat{k}\) - - -

The current element of the magnetic vector potential for a surface current will be a) J dS b) I dL c) K dS d) J dV

Description : The current element of the magnetic vector potential for a surface current will be a) J dS b) I dL c) K dS d) J dV

Last Answer : c) K dS

The magnetic vector potential for a line current will be inversely proportional to a) dL b) I c) J d) R

Description : The magnetic vector potential for a line current will be inversely proportional to a) dL b) I c) J d) R

Last Answer : d) R

The Laplacian of the magnetic vector potential will be a) –μ J b) – μ I c) –μ B d) –μ H

Description : The Laplacian of the magnetic vector potential will be a) –μ J b) – μ I c) –μ B d) –μ H

Last Answer : a) –μ J

Given the vector potential is 16 – 12sin y j. Find the field intensity at the origin. a) 28 b) 16 c) 12 d) 4

Description : Given the vector potential is 16 – 12sin y j. Find the field intensity at the origin. a) 28 b) 16 c) 12 d) 4

Last Answer : c) 12

Find the magnetic field intensity when the magnetic vector potential x i + 2y j + 3z k. a) 6 b) -6 c) 0 d) 1

Description : Find the magnetic field intensity when the magnetic vector potential x i + 2y j + 3z k. a) 6 b) -6 c) 0 d) 1

Last Answer : b) -6

Find the magnetic flux density of the material with magnetic vector potential A = y i + z j + x k. a) i + j + k b) –i – j – k c) –i-j d) –i-k

Description : Find the magnetic flux density of the material with magnetic vector potential A = y i + z j + x k. a) i + j + k b) –i – j – k c) –i-j d) –i-k

Last Answer : b) –i – j – k

Find the curl of the vector A = yz i + 4xy j + y k a) xi + j + (4y – z)k b) xi + yj + (z – 4y)k c) i + j + (4y – z)k d) i + yj + (4y – z)k

Description : Find the curl of the vector A = yz i + 4xy j + y k a) xi + j + (4y – z)k b) xi + yj + (z – 4y)k c) i + j + (4y – z)k d) i + yj + (4y – z)k

Last Answer : d) i + yj + (4y – z)k

Is the vector is irrotational. E = yz i + xz j + xy k a) Yes b) No

Description : Is the vector is irrotational. E = yz i + xz j + xy k a) Yes b) No

Last Answer : a) Yes

Find the curl of the vector and state its nature at (1,1,-0.2) F = 30 i + 2xy j + 5xz 2 k a) √4.01 b) √4.02 c) √4.03 d) √4.04

Description : Find the curl of the vector and state its nature at (1,1,-0.2) F = 30 i + 2xy j + 5xz 2 k a) √4.01 b) √4.02 c) √4.03 d) √4.04

Last Answer : d) √4.04

Find whether the vector is solenoidal, E = yz i + xz j + xy k a) Yes, solenoidal b) No, non-solenoidal c) Solenoidal with negative divergence d) Variable divergence

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Last Answer : a) Yes, solenoidal

Find the divergence of the vector F= xe -x i + y j – xz k a) (1 – x)(1 + e -x ) b) (x – 1)(1 + e -x ) c) (1 – x)(1 – e) d) (x – 1)(1 – e)

Description : Find the divergence of the vector F= xe -x i + y j – xz k a) (1 – x)(1 + e -x ) b) (x – 1)(1 + e -x ) c) (1 – x)(1 – e) d) (x – 1)(1 – e)

Last Answer : a) (1 – x)(1 + e -x )

Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates. a) (6.325,-71.57,3) b) (6.325,71.57,3) c) (6.325,73.57,3) d) (6.325,-73.57,3)

Description : Transform the vector B=yi+(x+z)j located at point (-2,6,3) into cylindrical coordinates. a) (6.325,-71.57,3) b) (6.325,71.57,3) c) (6.325,73.57,3) d) (6.325,-73.57,3)

Last Answer : a) (6.325,-71.57,3)

The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by a) (7,64.62,71.57) b) (7,-64.62,-71.57) c) (7,-64.62,71.57) d) (7,64.62,-71.57)

Description : The spherical equivalent of the vector B = yi + (x + z)j located at (-2,6,3) is given by a) (7,64.62,71.57) b) (7,-64.62,-71.57) c) (7,-64.62,71.57) d) (7,64.62,-71.57)

Last Answer : d) (7,64.62,-71.57)

Identify the correct vector identity. a) i . i = j . j = k . k = 0 b) i X j = j X k = k X i = 1 c) Div (u X v) = v . Curl(u) – u . Curl(v) d) i . j = j . k = k . i = 1

Description : Identify the correct vector identity. a) i . i = j . j = k . k = 0 b) i X j = j X k = k X i = 1 c) Div (u X v) = v . Curl(u) – u . Curl(v) d) i . j = j . k = k . i = 1

Last Answer : c) Div (u X v) = v . Curl(u) – u . Curl(v)

Find a vector normal to a plane consisting of points p1(0,1,0), p2(1,0,1) and p3(0,0,1) a) –j – k b) –i – j c) –i – k d) –i – j – k

Description : Find a vector normal to a plane consisting of points p1(0,1,0), p2(1,0,1) and p3(0,0,1) a) –j – k b) –i – j c) –i – k d) –i – j – k

Last Answer : a) –j – k

Rationalise the denominator in each of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236 up to three places of decimal. -Maths 9th

Description : Rationalise the denominator in each of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236 up to three places of decimal. -Maths 9th

Last Answer : Rationalisation of denominator

Rationalise the denominator in each of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236 up to three places of decimal. -Maths 9th

Description : Rationalise the denominator in each of the following and hence evaluate by taking √2 = 1.414, √3 = 1.732 and √5 = 2.236 up to three places of decimal. -Maths 9th

Last Answer : Rationalisation of denominator

A circle has radius √2 cm. It is divided into two segments by a chord of length 2cm.Prove that the angle subtended by the chord at a point in major segment is 45 degree . -Maths 9th

Description : A circle has radius √2 cm. It is divided into two segments by a chord of length 2cm.Prove that the angle subtended by the chord at a point in major segment is 45 degree . -Maths 9th

Last Answer : Given radius =2 cm Therefore AO=2 cm Let OD be the perpendicular from O on AB And AB =2cm Therefore AD=1cm (perpendicular from the centre bisects the chord) Now in triangle AOD, AO=2 cm ... by a chord at the centre is double of the angle made by the chord at any poin on the circumference)

If the length of a pendulum is doubled, its frequency of oscillation is changed by a factor of (a) 2 (b) √2 (c) 1/2 (d) 1/4

Description : If the length of a pendulum is doubled, its frequency of oscillation is changed by a factor of (a) 2 (b) √2 (c) 1/2 (d) 1/4

Last Answer : Ans:(c)

The ratio of the area of openings in one screen (Taylor series) to that of the openings in the next smaller screen is (A) 1.5 (B) 1 (C) √2 (D) None of these

Description : The ratio of the area of openings in one screen (Taylor series) to that of the openings in the next smaller screen is (A) 1.5 (B) 1 (C) √2 (D) None of these

Last Answer : (D) None of these

The ratio of the actual mesh dimension of Taylor series to that of the next smaller screen is (A) 2 (B) √2 (C) 1.5 (D) √3

Description : The ratio of the actual mesh dimension of Taylor series to that of the next smaller screen is (A) 2 (B) √2 (C) 1.5 (D) √3

Last Answer : (B) √2

Sphericity of a cubical particle, when its equivalent diameter is taken as the height of the cube, is (A) 0.5 (B) 1 (C) √2 (D) √3

Description : Sphericity of a cubical particle, when its equivalent diameter is taken as the height of the cube, is (A) 0.5 (B) 1 (C) √2 (D) √3

Last Answer : (B) 1

A column of length l is fixed at both ends. The equivalent length of the column is (A) l/2 (B) l/√2 (C) l (D) 2 l

Description : A column of length l is fixed at both ends. The equivalent length of the column is (A) l/2 (B) l/√2 (C) l (D) 2 l

Last Answer : (A) l/2

A shaft of length l carries two discs at its two ends. The lowest torsional frequency is ω n . If the shaft length is doubled, then the lowest torsional frequency becomes A ω n /2 B ω n /√2 C √2ω n D 2ω n

Description : A shaft of length l carries two discs at its two ends. The lowest torsional frequency is ω n . If the shaft length is doubled, then the lowest torsional frequency becomes A ω n /2 B ω n /√2 C √2ω n D 2ω n

Last Answer : B ω n /√2

In vibration isolation system, the transmissibility will be equal to unity, for all values of damping factor, if ω/ωn is A. Equal to 1 B. Equal to √2 C. Less than √2 D. Greater than √2

Description : In vibration isolation system, the transmissibility will be equal to unity, for all values of damping factor, if ω/ωn is A. Equal to 1 B. Equal to √2 C. Less than √2 D. Greater than √2

Last Answer : B. Equal to √2

In the graph shown below, the region in which frequency ratio (ω/ω n ) > √2 is known as____ A. Amplification region B. Isolation region C. Spring controlled region D. None of the above

Description : In the graph shown below, the region in which frequency ratio (ω/ω n ) > √2 is known as____ A. Amplification region B. Isolation region C. Spring controlled region D. None of the above

Last Answer : B. Isolation region

Consider the steady-state absolute amplitude equation shown below, if ω / ω n = √2 then amplitude ratio (X/Y) =? (X/Y) = √{1 + [ 2ξ (ω/ω n )] 2 } / √{[1 – (ω/ω n ) 2 ] 2 + {2ξ (ω/ω n ) 2 } A. 0 B. 1 C. less than 1 D. greater than 1

Description : Consider the steady-state absolute amplitude equation shown below, if ω / ω n = √2 then amplitude ratio (X/Y) =? (X/Y) = √{1 + [ 2ξ (ω/ω n )] 2 } / √{[1 – (ω/ω n ) 2 ] 2 + {2ξ (ω/ω n ) 2 } A. 0 B. 1 C. less than 1 D. greater than 1

Last Answer : B. 1

n vibration isolation system, if ω/ω n is less than √2 , then for all values of the damping factor, the transmissibility will be a) less than unity b) equal to unity c) greater than unity d) zero

Description : n vibration isolation system, if ω/ω n is less than √2 , then for all values of the damping factor, the transmissibility will be a) less than unity b) equal to unity c) greater than unity d) zero

Last Answer : c) greater than unity

Given that sin A=1/2 and cos B=1/√2 then the value of (A + B) is: (a)30 (b)45 (c)75 (d)60

Description : Given that sin A=1/2 and cos B=1/√2 then the value of (A + B) is: (a)30 (b)45 (c)75 (d)60

Last Answer : (c)75

Water is flowing at 1 m/sec through a pipe (of 10 cm I.D) with a right angle bend. The force in Newtons exerted on the bend by water is (A) 10 √2π (B) 5π/2 (C) 5 √2π (D) 5π/√2

Description : Water is flowing at 1 m/sec through a pipe (of 10 cm I.D) with a right angle bend. The force in Newtons exerted on the bend by water is (A) 10 √2π (B) 5π/2 (C) 5 √2π (D) 5π/√2

Last Answer : (B) 5π/2

A pipe of I.D. 4 m is bifurcated into two pipes of I.D. 2 m each. If the average velocity of water flowing through the main pipe is 5 m/sec, the average velocity through the bifurcated pipes is (A) 20 m/sec (B) 10 m/sec (C) 5 √2 m/sec (D) 5 m/sec

Description : A pipe of I.D. 4 m is bifurcated into two pipes of I.D. 2 m each. If the average velocity of water flowing through the main pipe is 5 m/sec, the average velocity through the bifurcated pipes is (A) 20 m/sec (B) 10 m/sec (C) 5 √2 m/sec (D) 5 m/sec

Last Answer : (B) 10 m/sec

According to maximum shear stress failure criterion, yielding in material occurs, when the maximum shear stress is equal to __________ times the yield stress. (A) 0.5 (B) 2 (C) √2 (D) √3/2

Description : According to maximum shear stress failure criterion, yielding in material occurs, when the maximum shear stress is equal to __________ times the yield stress. (A) 0.5 (B) 2 (C) √2 (D) √3/2

Last Answer : (A) 0.5

Evaluate: 2+√2 + 1/(2√2) + 1/(√2 - 2) a) 1 + 0.75√2 b) 2 + 1.5√2 c) 2 + √2 d) 2 - √2 e) None of these

Description : Evaluate: 2+√2 + 1/(2√2) + 1/(√2 - 2) a) 1 + 0.75√2 b) 2 + 1.5√2 c) 2 + √2 d) 2 - √2 e) None of these

Last Answer : 1/(√2 - 2) = (√2 + 2)/(2 - 4) = (√2 + 2)/ -2 1/(2√2) = √2/4 The given equation becomes: 2 + √2 +√2/4 – (√2 + 2) / 2 = (4(2 + √2) + √2 – 2(√2 + 2)) / 4 = (4 + 3√2) / 4 = 1 + 0.75√2 Answer: a)

4×(√3 + √4)2 + 6(√5 +√6)2 -3(√2 + √3)2 =? a) 167 b) 123 c) 157 d) 153 e) 149

Description : 4×(√3 + √4)2 + 6(√5 +√6)2 -3(√2 + √3)2 =? a) 167 b) 123 c) 157 d) 153 e) 149

Last Answer : ? =4(3+4+2√12) + 6(5+6+2√30)-3(2+3+2√6) =4(7+2√12)+6(11+2√30)-3(5+2√6) =28 + 8√12 + 66 + 12√30 – 15 - 6√6 =(28+66-15) + (8√12+12√30-6√6) =79 + (8√4 × 3 + 12√30 - 6√6) =79+16√3 + 12√30 - 6√6 =79 + 16 ×1.7 + 12 × 5.4 – 6 ×2.4 =79+27.2 + 64.8-14.4 = 156.6 = 157 Answer: c)

A proton and a deuteron have same kinetic energies while moving in a perpendicular magnetic field. The following gives the ratio of radii of their circular paths a) √2 : 1 b) 1: √2 c) 1:4 d) 1:1

Description : A proton and a deuteron have same kinetic energies while moving in a perpendicular magnetic field. The following gives the ratio of radii of their circular paths a) √2 : 1 b) 1: √2 c) 1:4 d) 1:1

Last Answer : b) 1: √2

A proton having mass m and charge q is projected into a region having a perpendicular magnetic field. The angle of deviation of proton when it comes out of the region with mv √2 qB ⁄ is a) π/3 b) π/4 c) π/6 d) 2 π/3

Description : A proton having mass m and charge q is projected into a region having a perpendicular magnetic field. The angle of deviation of proton when it comes out of the region with mv √2 qB ⁄ is a) π/3 b) π/4 c) π/6 d) 2 π/3

Last Answer : b) π/4

A proton moves in a uniform magnetic field in a circular path of radius R. If the energy of proton is doubled then the new radius becomes a) R √2 b) 2R c) R 2 d) √2 R

Description : A proton moves in a uniform magnetic field in a circular path of radius R. If the energy of proton is doubled then the new radius becomes a) R √2 b) 2R c) R 2 d) √2 R

Last Answer : d) √2 R

The sum of a positive number and its reciprocal is twice the difference of the number and its reciprocal. The number is : (A) √2 (B) 1/√2 (C) √3 (D) 1/√3

Description : The sum of a positive number and its reciprocal is twice the difference of the number and its reciprocal. The number is : (A) √2 (B) 1/√2 (C) √3 (D) 1/√3

Last Answer : Answer: C

Consider a triangle A(0, 0), B(1, 1), C(5, 2). The triangle has to be rotated by an angle of 450 about the point P(-1, -1). What shall be the coordinates of the new triangle? (A) A'=(1, √2-1), B'=(-1, 2√2-1), C'=(3√2-1, (9/2)√2-1) (B) A'=(1, √2-1), B'=(2√2-1, -1), C'=(3√2-1, (9/2)√2-1) (C) A'=(-1, √2-1), B'=(-1, 2√2-1), C'=(3√2-1, (9/2)√2-1) (D) A'=(√2-1, -1), B'=(-1, 2√2-1), C'=(3√2-1, (9/2)√2-1)

Description : Consider a triangle A(0, 0), B(1, 1), C(5, 2). The triangle has to be rotated by an angle of 450 about the point P(-1, -1). What shall be the coordinates of the new triangle? (A) A'=(1, √2-1), B'=(-1, 2√2-1), C'=(3√2-1, ... 3√2-1, (9/2)√2-1) (D) A'=(√2-1, -1), B'=(-1, 2√2-1), C'=(3√2-1, (9/2)√2-1)

Last Answer : (C) A'=(-1, √2-1), B'=(-1, 2√2-1), C'=(3√2-1, (9/2)√2-1)

Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by the two vectors.

Description : Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by the two vectors.

Last Answer : Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by the two vectors.

Plasmid has been used as vector because (a) it is circular DNA which have capacity to join to eukaryotic DNA (b) it can move between prokaryotic and eukaryotic cells (c) both ends show replication (d) it has antibiotic resistance gene.

Description : Plasmid has been used as vector because (a) it is circular DNA which have capacity to join to eukaryotic DNA (b) it can move between prokaryotic and eukaryotic cells (c) both ends show replication (d) it has antibiotic resistance gene.

Last Answer : (a) it is circular DNA which have capacity to join to eukaryotic DNA

Explain Unit Vector.

Description : Explain Unit Vector.

Last Answer : In kinematics, a unit vector is a vector with a magnitude of 1. It is a vector that has been normalized, meaning it has been divided by its own magnitude, resulting in a vector that points in ... for analyzing the motion of an object in space and for determining how an object is moving and rotating.