Question

Given \(\vec{OP}=3\vec{a}-2\vec{b}\) and \(\vec{OQ}=\vec{a}+\vec{b}\), what is \(\vec{OR}\) when \(R\) divides \(PQ\) externally in the ratio \(2:1\)?

Options

• \[\vec{OR}=4\vec{b}-\vec{a}\]

• \[\vec{OR}=\frac{5\vec{a}}{3}\]

• \[\vec{OR}=\frac{5\vec{a}-4\vec{b}}{3}\]

• \[\vec{OR}=\vec{a}+4\vec{b}\]

Answer 1

For external division in the ratio \(2:1\), use \(\frac{2(\vec{a}+\vec{b})-(3\vec{a}-2\vec{b})}{2-1}\). Simplifying gives \(4\vec{b}-\vec{a}\).