Question

$a$ and $b$ are non-collinear vectors. If $c=(x-2)a+b$ and $d=(2x+1)a-b$ are collinear vectors, then the value of $x=......$

• A. $\frac{1}{2}$
• B. $\frac{1}{4}$
• C. $\frac{1}{5}$
• D. $\frac{1}{3}$

Answer 1

Answer: (D)

Given, $c=(x-2)a+b$ and
$d=(2x+1)a-b$ are collinear
$\therefore c=\lambda d$
$\Rightarrow (x-2)a+b=\lambda [(2x+1)a-b]$
$\Rightarrow \frac{x-2}{2x+1}=\frac{1}{-1}=\lambda$
$\Rightarrow 2x+1=-x+2$
$\Rightarrow 3x=1$
$\Rightarrow x=\frac{1}{3}$