Question

Show that the points having position vectors, $\overline{a},\overline{b}$ and $3\overline{a}-2\overline{b}$ are colliera, where $\overline{a},\overline{b},\overline{c}$ any vectors.

Answer 1

Let given vectors $\underset{A}{\overline{a}},\underset{B}{\overline{b}},\underset{C}{3\overline{a}-2\overline{b}}$

$\overline{AB}=\overline{b}-\overline{a}$

$\overline{AC}=3\overline{a}-2\overline{b}-\overline{a}=2\overline{a}-2\overline{b}$

$\overline{AC}=-2\overline{AB}$

Here $\overline{a},\overline{b},3\overline{a}-2\overline{b}$ are collinear