Question

# $$P,Q$$ have position vectors $$\overrightarrow { a }$$ and $$\overrightarrow { b }$$ relative to the origin $$O$$ and $$X,Y$$ divide $$\overrightarrow { OQ }$$ internally and externally respectively in the ratio $$2:1$$. Vector $$\overrightarrow { XY }=$$

A
32(ba)
B
34(ba)
C
56(ba)
D
43(ba)

Solution

## The correct option is B $$\displaystyle \dfrac { 4 }{ 3 } \left( \overrightarrow { b } -\overrightarrow { a } \right)$$P.V. of $$\displaystyle x=\dfrac { \overrightarrow { a } +2\overrightarrow { b } }{ 3 }$$P.V. of $$\displaystyle y=\dfrac { 2\overrightarrow { b } -\overrightarrow { a } }{ 1 }$$$$\displaystyle \overrightarrow { XY } =2\overrightarrow { b } -\overrightarrow { a } -\dfrac { \overrightarrow { a } +2\overrightarrow { b } }{ 3 } =\dfrac { 4\overrightarrow { b } }{ 3 } -\dfrac { 4\overrightarrow { a } }{ 3 } =\dfrac { 4 }{ 3 } \left( \overrightarrow { b } -\overrightarrow { a } \right)$$Mathematics

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