Question

Two vectors $\overrightarrow{A}+\overrightarrow{B}$ have equal magnitudes. If magnitude of $\overrightarrow{A}+\overrightarrow{B}$ is equal to two times the magnitude of $\overrightarrow{A}-\overrightarrow{B}$ then the angle between vec A and $\overrightarrow{B}$ will be

• A. $sin^{-1}(\frac{3}{5})$
• B. $sin^{-1}(\frac{1}{3})$
• C. $sin^{-1}(\frac{3}{5})$
• D. $sin^{-1}(\frac{1}{3})$

Answer 1

Answer: (C)

$sin^{-1}(\frac{3}{5})$

Answer 2

The correct option is(C): $cos^{-1}(\frac{3}{5})$

$\sqrt{A^2+A^2+2A^2\,cosθ}=2\sqrt{A^2+2A^2(-cosθ))}$

⇒ 2 A 2 + 2 A 2cos θ = 8 A 2 + 8 A 2(–cos θ)

⇒ 5cos θ = 3

$⇒ θ =cos^{-1}(\frac{3}{5})$