Question

Two vectors $\overrightarrow{A}$ and $\overrightarrow{B}$ are such that $\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}$ and $A^2+B^2=C^2.$ If $\theta$ is the angle between positive direction of $\overrightarrow{A}$ and $\overrightarrow{B}$ then the correct statement is (given $\overrightarrow{A}$ and $\overrightarrow{B}$ are not zero vector)

• A. $\theta =\pi$
• B. $\theta =\frac{2\pi }{3}$
• C. $\theta =0$
• D. $\theta =\frac{\pi }{2}$

Answer 1

The correct option is D $\theta =\frac{\pi }{2}$

$\overrightarrow{A}+\overrightarrow{B}=\overrightarrow{C}⟹C=\sqrt{A^2+B^2+2ABcos\theta }$
Given, $A^2+B^2=C^2$, thus $2ABcos\theta =0$.
Since $\overrightarrow{A}$ and $\overrightarrow{B}$ are not zero vectors, thus $cos\theta =0or\theta ={90}^0$.