Question

If the vectors $2\overline{i}-q\overline{j}+3\overline{k}$ and $4\overline{i}-5\overline{j}+6\overline{k}$ are collinear, then value of q is

• A. $5$
• B. $10$
• C. $\frac{5}{2}$
• D. $\frac{5}{4}$

Answer 1

The correct option is C $\frac{5}{2}$

Let $\overrightarrow{a}=2\hat{i}-q\hat{j}+3\hat{k}$ and $\overrightarrow{b}=4\hat{i}-5\hat{j}+6\hat{k}$

Since $\overrightarrow{a}$ and $\overrightarrow{b}$ are collinear.

$\therefore$ thereexists a scalar $t$ such that $\overrightarrow{b}=t\overrightarrow{a}$

$\therefore 4\hat{i}-5\hat{j}+6\hat{k}=t(2\hat{i}-q\hat{j}+3\hat{k})$

$\therefore 4\hat{i}-5\hat{j}+6\hat{k}=2t\hat{i}-qt\hat{j}+3t\hat{k}$

$\therefore$ By equality of vectors, we get

$4=2t\Rightarrow t=2$

$\Rightarrow -qt=-5$ or $qt=5$

$\Rightarrow 2q=5$ or $q=\frac{5}{2}$