Three points whose position vectors are a + b, , ,a - b and a + k… - Vidyadip

MCQ

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

A
Zero
B
Only negative real number
C
Only positive real number
✓
Every real number

✓

Answer

Correct option: D.

Every real number

d
(d) $\overrightarrow {AB} = \lambda \overrightarrow {BC} $, (for collinearity)

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

Hence $\forall \,\,k \in R \Rightarrow \overrightarrow {AB} = \lambda \overrightarrow {BC} .$

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