Question

If the points $\mathbf{a} + \mathbf{b},\mathbf{a} - \mathbf{b}$ and $\mathbf{a} + k\mathbf{b}$ be collinear, then k =

• A. 0
• B. 2
• C. – 2
• D. Any real number

Answer 1

Answer: (D)

Any real number

Answer 2

$(\mathbf{a} - \mathbf{b}) - (\mathbf{a} + \mathbf{b}) = \left\lbrack (\mathbf{a} + k\mathbf{b}) - (\mathbf{a} - \mathbf{b}) \right\rbrack$

$\Rightarrow - 2\mathbf{b} = (k + 1)\mathbf{b}$. Hence $k \in R.$