Question

The unit vector in the direction of resultant of two vectors with components $(2,4,-5)$ and $(1,2,3)$ is:

• A. $\frac{3\hat{i}+6\hat{j}+2\hat{k}}{49}$
• B. $\frac{3\hat{i}+6\hat{j}+2\hat{k}}{7}$
• C. $\frac{3\hat{i}}{7}+\frac{6\hat{j}}{7}-\frac{2\hat{k}}{7}$
• D. $\frac{3\hat{i}+6\hat{j}-2\hat{k}}{49}$

Answer 1

The correct option is C $\frac{3\hat{i}}{7}+\frac{6\hat{j}}{7}-\frac{2\hat{k}}{7}$

$\overrightarrow{A}$ + $\overrightarrow{B}$ = $3\hat{i}+6\hat{j}-2\hat{k}$
To make it a unit vector , we'll have to divide it by it's magnitude which is $7$.
Hence, the unit vector is, $\frac{3i+6j-2k}{7}$