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Physics Vectors Mix Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: September 12, 2026

At what angle must the two forces (x + y) and (x – y) act so that the resultant may be \(\sqrt{x^{2} + y^{2}}\)

\(\cos^{-1}\left(-\frac{x^{2}-y^{2}}{2(x^{2}+y^{2})}\right)\)

\(\cos^{-1}\left(-\frac{2(x^{2}-y^{2})}{x^{2}+y^{2}}\right)\)

\(\cos^{-1}\left(-\frac{x^{2}+y^{2}}{x^{2}-y^{2}}\right)\)

\(\cos^{-1}\left(-\frac{x^{2}-y^{2}}{x^{2}+y^{2}}\right)\)

Text Solution

Verified by Experts

The correct answer is:

\(R^2 = A^2 + B^2 + 2AB \cos \theta\)

Substituting, \(\mathbf{A} = (x + y)\) , \(\mathbf{B} = (\mathbf{x} - \mathbf{y})\) and \(\mathbf{R} = \sqrt{x^{2} + y^{2}}\)

we get \(\theta = \cos^{-1} \left( - \frac{x^{2} + y^{2}}{2(x^{2} - y^{2})} \right)\)

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