If $|\vec{a}|=7$ then $|3 \vec{a}|$ is :

CUET Preparation Today

Start Free Mocks

Home Questions 5GDFXR5SCN

Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Determinants

Question:

If $|\vec{a}|=7$ then $|3 \vec{a}|$ is :

Options:

$\sqrt{21}$

Correct Answer:

Explanation:

$|\vec{a}|$ = 7 $|3 \vec{a}|$ = ?

let $\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$

so $|\vec{a}|=\sqrt{a_1^2+a_2^2+a_3^2}$

so $|3 \vec{a}|=\sqrt{9 a_1^2+9 a_2^2+9 a_3^2} \Rightarrow 3 \sqrt{a_1^2+a_2^2+a_3^2}$

so $|3 \vec{a}|=3|\vec{a}|$

so $\Rightarrow 21$