The vector in the direction of the vector $\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}}$ that has magnitude 9 is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $3(\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}})$ ##
Let $\mathbf{a} = \hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}}$
Any vector in the direction of a vector $\mathbf{a}$ is given by $\frac{\mathbf{a}}{|\mathbf{a}|}$
$= \frac{\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}}}{\sqrt{1^2 + 2^2 + 2^2}} = \frac{\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}}}{3}$
$∴$ Vector in the direction of $\mathbf{a}$ with magnitude $9 = 9 \cdot \frac{\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}}}{3}$
$= 3(\hat{\mathbf{i}} - 2\hat{\mathbf{j}} + 2\hat{\mathbf{k}})$