Question

If $\overrightarrow{a}$ and $\overrightarrow{b}$ are the position vectors of A and B, respectively, find the position vector of a point C in BA produced such that BC = 1.5 BA.

Answer 1

Since $\overline{OA}=\overline{a}$ and $\overline{OB}=\overline{b}$

$\therefore \overline{BA}=\overline{OA}-\overline{OB}=\overline{a}-\overline{b}$

And $1.5\overline{BA}=1.5(\overline{a}-\overline{b})$

Since, $\overline{BC}=1.5\overline{BA}=1.5(\overline{a}-\overline{b})$

$\overline{OC}-\overline{OB}=1.5\overline{a}-1.5\overline{b}$

$\overline{OC}=1.5\overline{a}-1.5\overline{b}+b[\because \overline{OB}=\overline{b}]$

$=1.5\overline{a}-0.5\overline{b}$

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

Graphically, explanation of the above solution is given above