Question

Given two vectors $\overrightarrow{A}=\hat{i}-2\hat{j}-3\hat{k}$ and $\overrightarrow{B}=4\hat{i}-2\hat{j}+6\hat{k}$, the angle made by $(\overrightarrow{A}+\overrightarrow{B})$ with x-axis is:

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

Answer 1

Answer: (B)

${45}^o$

$(\overrightarrow{A}+\overrightarrow{B})=5\hat{i}-4\hat{j}+3\hat{k}$
The angle made by $(\overrightarrow{A}+\overrightarrow{B})$ and x-axis is $\theta ={\cos }^{-1}\left(\right((\overrightarrow{A}+\overrightarrow{B}).\hat{i}\left)/|\right(\overrightarrow{A}+\overrightarrow{B}\left)||\hat{i}|\right)=\frac{5}{\sqrt{5^2+4^2+3^2}.1}={45}^0$