Vector in the direction of $\hat{i}+\hat{j}+\hat{k}$ with magnitude 5 units is :
Answer & explanation
Correct answer: option 3
$\vec{v} = \hat{i}+\hat{j}+\hat{k}$
$|\vec{v}| = \sqrt{1^2+1^2+1^2} = \sqrt{3}$
unit vector $\hat{v} = \frac{\vec{v}}{|\vec{v}|}$
⇒ vector of magnitude 5 in direction of $\vec{v}$ is $5 \hat{v} = \frac{5\vec{v}}{|\vec{v}|}$
⇒ $\frac{5(\hat{i}+\hat{j} + \hat{k})}{\sqrt{3}}$