The acute angle which the perpendicular from the origin on the line 7x –3y = 4 makes with the x-axis is: -Maths 9th

The acute angle which the perpendicular from the origin on the line 7x –3y = 4 makes with the x-axis is: -Maths 9th
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Answer :

(c) negativeAs the line from the origin is perpendicular to the line 7x – 3y = 4, so its slope = \(rac{-1}{ ext{slope of }\,7x-3y=4}\)Slope of 7x – 3y – 4 = \(rac{7}{3}\)∴ Slope of line from origin = \(rac{-1}{+rac{7}{3}}\) = \(rac{-3}{7}\)∴ tan θ = \(rac{-3}{7}\), where θ is the angle the line makes with the +ve direction of x-axis⇒ θ = tan-1 \(\big(rac{-3}{7}\big)\) = - tan-1 \(\big(rac{3}{7}\big)\)
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