CGP Edu

Physics Vectors Mix Single Correct MCQ

Published on: September 12, 2026

If \vec{A} = 2\hat{i} + 3\hat{j} - \hat{k} and \vec{B} = -\hat{i} + 3\hat{j} + 4\hat{k} then projection of \vec{A} on \vec{B} will be

\(\frac{3}{\sqrt{13}}\)

\(\frac{3}{\sqrt{26}}\)

\(\sqrt{\frac{3}{26}}\)

\(\sqrt{\frac{3}{13}}\)

Text Solution

Verified by Experts

The correct answer is:

\(\left|\vec{A}\right| = \sqrt{2^2 + 3^2 + (-1)^2} = \sqrt{4 + 9 + 1}\) \(= \sqrt{14}\)

\(\left|\vec{B}\right| = \sqrt{(-1)^2 + 3^2 + 4^2}\) \(= \sqrt{1 + 9 + 16}\) \(= \sqrt{26}\)

\(\vec{A} \cdot \vec{B} = 2(-1) + 3 \times 3 + (-1)(4) = 7\)

The projection of \(\vec{A} \text{ on } \vec{B}\) \(= \frac{\vec{A} \cdot \vec{B}}{|\vec{B}|}\) \(= \frac{3}{\sqrt{26}}\)

Previous Question Next Question

Get practice questions, solutions, and test series in one place.

Share your experience with this question and solution.

Send your comment, doubt, correction, or feedback to admin.

What students say about this solution

No reviews yet. Be the first to write a review.