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Vectors — Maths STD 12 Science — Question

Maharashtra BoardEnglish MediumSTD 12 ScienceMathsVectors2 Marks
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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