Question

If $\overline{a}=\hat{i}-\hat{j}+\hat{k}$ and $\overline{b}=2\hat{i}-\hat{j}+3\hat{k}$, then the unit vector along $\overline{a}+\overline{b}$ is

• A. $\frac{3\hat{i}+4\hat{k}}{5}$
• B. $\frac{-3\hat{i}+4\hat{k}}{5}$
• C. $\frac{-3\hat{i}-4\hat{k}}{5}$
• D. $noneofthese$

Answer 1

The correct option is D $noneofthese$

$\overrightarrow{b}=2\hat{i}-\hat{j}+3\hat{k}$

$\overrightarrow{a}=\hat{i}-\hat{j}+\hat{k}$

$\overrightarrow{a}+\overrightarrow{b}=3\hat{i}-2\hat{j}+4\hat{k}$

Unit vector along AB is $\frac{1}{3^2+2^2+4^2}3\hat{i}-2\hat{j}+4\hat{k}=\frac{1}{29}3\hat{i}-2\hat{j}+4\hat{k}$