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  • The position vectors of two points A and B are <img alt="\overrightarrow{OA}=2\widehat{i}-\widehat{j}-\widehat{k}" src="https://learn.careers360.com/latex-image/?%5Coverrightarrow%7BOA%7D%3D2%5Cwidehat%7Bi%7D-%5Cwidehat%7Bj%7D-%5Cwidehat%7Bk%7D" /

The position vectors of two points A and B are \overrightarrow{OA}=2\widehat{i}-\widehat{j}-\widehat{k}  and \overrightarrow{OB}=2\widehat{i}-\widehat{j}+2\widehat{k}, respectively. The position vector of a point P which divides the line segment joining A and B in the ratio 2 : 1 is ___________ .

 

 
 
 
 
 

Answers (1)

Given: 

\overrightarrow{OA}=2\widehat{i}-\widehat{j}-\widehat{k}  

\overrightarrow{OB}=2\widehat{i}-\widehat{j}+2\widehat{k}

\\ \overrightarrow{OP}=\frac{2 \overrightarrow{OB}+\overrightarrow{OA}}{3}\\\\ = \frac{2(2\widehat{i}-\widehat{j}+2\widehat{k})+2\widehat{i}-\widehat{j}-\widehat{k}}{3}\\\\ = 2\widehat{i}-\widehat{j}+\widehat{k}

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Safeer PP

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