Question

If the points $a+b$ , $a-b$ and $a-kb$ are collinear then value of $k$ is equal to :

• A. $0$
• B. $2$
• C. $-2$
• D. Any real number

Answer 1

The correct option is D Any real number

Given vectors

$\overrightarrow{p}=a+b$

$\overrightarrow{q}=a-b$

$\overrightarrow{r}=a-kb$

then condition for colinear vectors

$\overrightarrow{pq}+\overrightarrow{qr}=\overrightarrow{pr}$

$a-b-a-b+a-kb-a+b=a-kb-a-b$

$a-b-a-b+a-kb-a+b=a-kb-a-b$

$-(1+k)b=-(1+k)b$

here the $\overrightarrow{b}$ is not depend on the value of $k$

So $k$may be real number