Question

The vector having magnitude of 12 units in the direction of the $\overrightarrow{A}=3\hat{i}+2\hat{j}-6\hat{k}$
is

• A. $36\hat{i}+24\hat{j}-72\hat{k}$
• B. $\frac{(36\hat{i}+24\hat{j}-72\hat{k})}{7}$
• C. $12\hat{i}+12\hat{j}-12\hat{k}$
• D. $\frac{(3\hat{i}+2\hat{j}-6\hat{k})}{7}$

Answer 1

The correct option is B $\frac{(36\hat{i}+24\hat{j}-72\hat{k})}{7}$

We need vector in the direction of $3\hat{i}+2\hat{j}-6\hat{k}$, so first we will calculate the unit vector in the direction of the given vector
$\hat{A}=\frac{\overrightarrow{A}}{|\overrightarrow{A}|}=\frac{3\hat{i}+2\hat{j}-6\hat{k}}{\sqrt{3^2+2^2+(-6{)}^2}}=\frac{3\hat{i}+2\hat{j}-6\hat{k}}{7}$

Now on multiplying the unit vector with the magnitude, we will get the required vector.
$12\times \frac{3\hat{i}+2\hat{j}-6\hat{k}}{7}=\frac{36\hat{i}+24\hat{j}-72\hat{k}}{7}$
so, option B is the correct answer.