Question

Let $\overrightarrow{\alpha }=(\lambda -2)\overrightarrow{a}+b$ and $\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}$ be two given vectors where vectors $\overrightarrow{a}$ and $\overrightarrow{b}$ non-collinear. The value of $\lambda$ for which vectors $\overrightarrow{\alpha }$ and $\overrightarrow{\beta }$ are collinear, is :

• A. $-3$
• B. $4$
• C. $3$
• D. $-4$

Answer 1

The correct option is D $-4$

$\overrightarrow{\alpha }=(\lambda -2)\overrightarrow{a}+b$

$\overrightarrow{\beta }=(4\lambda -2)\overrightarrow{a}+3\overrightarrow{b}$

$\frac{\lambda -2}{4\lambda -2}$=$\frac{1}{3}$

$3\lambda -6=4\lambda -2$

$\lambda =-4$