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