Question

The three points with position vectors $\overline{a}+\overline{b},\overline{a}-\overline{b}$ and $\overline{a}+\lambda \overline{b}$ are collinear for

• A. no value of λ
• B. exactly one value of λ
• C. exactly two values of λ
• D. many values of λ

Answer 1

The correct option is D

many values of λ

Let $\overline{OP}=\overline{a}+\overline{b},\overline{OQ}=\overline{a}-\overline{b},\overline{OR}=\overline{a}+\lambda \overline{b}$

$\overline{PQ}=-2\overline{b},\overline{PR}=(\lambda -1)\overline{b}\Rightarrow$ many values of $\lambda$