Question

Three points whose position vectors are $\mathbf{a} + \mathbf{b},\mathbf{a} - \mathbf{b}$ and $\mathbf{a} + k\mathbf{b}$ will be collinear, if the value of k is

• A. Zero
• B. Only negative real number
• C. Only positive real number
• D. Every real number

Answer 1

Answer: (D)

Every real number

Answer 2

$\overset{\rightarrow}{AB} = \lambda\overset{\rightarrow}{BC}$, (for collinearity)

Here $\overset{\rightarrow}{AB} = - 2\mathbf{b},$ $\overset{\rightarrow}{BC} = (k + 1)\mathbf{b}$

Hence $\forall k \in R \Rightarrow \overset{\rightarrow}{AB} = \lambda\overset{\rightarrow}{BC}.$