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

MCQ

Three points whose position vectors are $\bar{a}+\bar{b}$, $\overline{ a }-\overline{ b }$ and $\overline{ a }+ k \overline{ b }$ are collinear, then 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) Let $A , B , C$ be the three collinear point.
$\therefore \quad \overline{ AB }=\lambda \overline{ BC }$
Here, $\overline{A B}=-2 b, \overline{B C}=(k+1) \bar{b}$
$\therefore \forall k \in R \Rightarrow \overline{ AB }=\lambda \overline{ BC }$

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