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Physics Vectors Fundamentals of Vectors Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: September 12, 2026

If \vec{A} = 2\hat{i} + 4\hat{j} - 5\hat{k} the direction of cosines of the vector \vec{A} are

\(\frac{2}{\sqrt{45}}, \frac{4}{\sqrt{45}}\) and \(\frac{-5}{\sqrt{45}}\)

\(\frac{1}{\sqrt{45}}, \frac{2}{\sqrt{45}}\) and \(\frac{3}{\sqrt{45}}\)

\(\frac{4}{\sqrt{45}}, 0\) and \(\frac{4}{\sqrt{45}}\)

\(\frac{3}{\sqrt{45}}, \frac{2}{\sqrt{45}}\) and \(\frac{5}{\sqrt{45}}\)

Text Solution

Verified by Experts

The correct answer is:

\vec{A} = 2\hat{i} + 4\hat{j} - 5\hat{k}

\(\therefore |\vec{A}| = \sqrt{(2)^2 + (4)^2 + (-5)^2} = \sqrt{45}\)

\(\therefore \cos \alpha = \frac{2}{\sqrt{45}}, \cos \beta = \frac{4}{\sqrt{45}}, \cos \gamma = \frac{-5}{\sqrt{45}}\)

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