alleryIf $\vec a, \vec b, \vec c$ are the position vectors of $A, B, C$ and $5\vec a - 3\vec b - 2\vec c = \vec 0$, then point $C$ divides $\overline{BA}$:
AInternally in ratio 5:3
BExternally in ratio 5:3
CInternally in ratio 3:5
DExternally in ratio 3:5
Answer & Solution
Correct answer: B. Externally in ratio 5:3
**From the relation:** $2\vec c = 5\vec a - 3\vec b$
⇒ $\vec c = (5\vec a - 3\vec b)/2 = (5\vec a - 3\vec b)/(5 - 3)$.
This matches the external division formula $\vec r = (m\vec A - n\vec B)/(m - n)$ with $m = 5, n = 3$
so $C$ divides $\overline{BA}$ externally in ratio 5:3.
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