Question

If the vectors $\overline{a}=2\overline{i}+3\overline{j}+6\overline{k}$ and $\overline{b}$ are collinear and $|\overline{b}|=21$, then $\overline{b}$ equals to

• A. $\pm 2(2\overline{i}+3\overline{j}+6\overline{k})$
• B. $\pm 3(2\overline{i}+3\overline{j}+6\overline{k})$
• C. $\overline{i}+\overline{j}\overline{k}$
• D. $\pm 21(2\overline{i}+3\overline{j}+6\overline{k})$

Answer 1

The correct option is D $\pm 21(2\overline{i}+3\overline{j}+6\overline{k})$

Given that,

$\overline{a}=2\overline{i}+3\overline{j}+6\overline{k}$

$\left|\overline{b}\right|=21\left[\because \overline{a}=\lambda \overline{b}\right]$

Collinear

$\pm 21\left(2\overline{i}+3\overline{j}+6\overline{k}\right)$

Option $\left(D\right)$ is correct answer.