Practicing Success

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

Vector in the direction of $\hat{i}+\hat{j}+\hat{k}$ with magnitude 5 units is :

Options:

$\frac{\hat{i}-\hat{j}+\hat{k}}{\sqrt{3}}$

$\frac{\hat{i}+\hat{j}+\hat{k}}{\sqrt{3}}$

$\frac{5(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}}$

$\frac{5}{3}(\hat{i}+\hat{j}+\hat{k})$

Correct Answer:

$\frac{5(\hat{i}+\hat{j}+\hat{k})}{\sqrt{3}}$

Explanation:

$\vec{v} = \hat{i}+\hat{j}+\hat{k}$

$|\vec{v}| = \sqrt{1^2+1^2+1^2} = \sqrt{3}$

unit vector $\hat{v} = \frac{\vec{v}}{|\vec{v}|}$ 

⇒ vector of magnitude 5 in direction of $\vec{v}$ is $5 \hat{v} = \frac{5\vec{v}}{|\vec{v}|}$

⇒ $\frac{5(\hat{i}+\hat{j} + \hat{k})}{\sqrt{3}}$