Discussion Forum

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

Answer:

Explanation:

 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= $\frac{1}{3}$