Question

Given two vectors $A\to =-\widehat{i}+2\widehat{j}-3\widehat{k}$ and $B\to =4\widehat{i}+2\widehat{j}-6\widehat{k}.$ . The angle made by $(A\to +B\to )$ with x-axis is

• A. $30{}^\circ$
• B. $45{}^\circ$
• C. $60{}^\circ$
• D. $90{}^\circ$

Answer 1

Answer: (B)

$45{}^\circ$

Answer 2

Given, $\vec{A}=-\hat{i}+2\hat{j}-3\hat{k}$ $\hat{B}=4\hat{i}-2\hat{j}+6\hat{k}$ Let angle made by $(\vec{A}+\vec{B})$ with $x-$ axis is $\theta .$ $\cos \theta =\frac{(\vec{A}+\vec{B}).\hat{i}}{|\vec{A}+\vec{B}|.|\hat{i}|}=\frac{(3\hat{i}+3\hat{k}).\hat{i}}{\sqrt{9+9}.1}$ $=\frac{3}{3\sqrt{2}}=\frac{1}{\sqrt{2}}$ $\therefore$ $\theta ={{45}^{o}}$