A point C with position vector 3a+4b-5c 3 (where a, b and c are n…

MCQ

A point C with position vector $\frac{\text{3a}+4\text{b}-5\text{c}}{3}$ (where a, b and c are non co-planar vectors) divides the line joining A and B in the ratio 2 : 1. If the position vector of A is a - 2b + 3c, then the position vector of B is:

A
2a + 3b - 4c
B
2a - 3b + 4c
C
2a + 3b + 4c
✓
a + 3b - 4c

✓

Answer

Correct option: D.

a + 3b - 4c

a - 2b + 3c
$\frac{\text{3a}+4\text{b}-5\text{c}}{3}$
$\overrightarrow{\text{c}}=\frac{2\overrightarrow{\text{b}}+\overrightarrow{\text{a}}}{3}$
$\overrightarrow{\text{b}}=\frac{3\overrightarrow{\text{c}}-\overrightarrow{\text{a}}}{2}$
$=\frac{\big(3\overrightarrow{a}+4\overrightarrow{b}-5\overrightarrow{c}\big)-\big(\overrightarrow{a}+2\overrightarrow{b}-3\overrightarrow{c}\big)}{2}$
$=\overrightarrow{a}+3\overrightarrow{b}-4\overrightarrow{c}$

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