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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)
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B
34(ba)
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C
56(ba)
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D
43(ba)
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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 $$\displaystyle y=\dfrac { 2\overrightarrow { b } -\overrightarrow { a }  }{ 1 } $$
$$\displaystyle \overrightarrow { XY } =2\overrightarrow { b } -\overrightarrow { a } -\dfrac { \overrightarrow { a } +2\overrightarrow { b }  }{ 3 } =\dfrac { 4\overrightarrow { b }  }{ 3 } -\dfrac { 4\overrightarrow { a }  }{ 3 } =\dfrac { 4 }{ 3 } \left( \overrightarrow { b } -\overrightarrow { a }  \right) $$

403104_120354_ans.PNG

Mathematics

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