The position vector of the point which divides the join of the points \( 2\vec{a}-3\vec{b} \) and \( 3\vec{a}-2\vec{b} \) externally in the ratio 2: 3, is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \( -5\vec{b} \)
For external division of the join of \( \vec{p} \) and \( \vec{q} \) in the ratio m : n, the position vector is \( \frac{m\vec{q}-n\vec{p}}{m-n} \). Here m : n = 2 : 3.
\( \displaystyle \frac{2(3\vec{a}-2\vec{b})-3(2\vec{a}-3\vec{b})}{2-3} \)
\( \displaystyle =\frac{6\vec{a}-4\vec{b}-6\vec{a}+9\vec{b}}{-1} \)
\( \displaystyle =\frac{5\vec{b}}{-1} \)
\( =-5\vec{b} \)