X and Y are two points with position vectors 3\, \vec{a}+\vec{b} and \vec{a}-3\: \vec{b} redpectively. Write the position vector of a point Z which divides the line segment XY in the ratio 2 : 1 externally.

 

 

 

 
 
 
 
 

Answers (1)

here \overrightarrow{OX}= 3\vec{a}+\vec{b}      and     \overrightarrow{OY}= \vec{a}-3\vec{b}
As Z which divides the line segment XY in the ratio 2:1 externally
\therefore \overrightarrow{OZ}= \frac{2\overrightarrow{OY}-\overrightarrow{OX}}{2-1}\: \: = \frac{2\left ( \vec{a}-3\vec{b}\right )-\left ( 3\vec{a}+\vec{b} \right )}{1}=-\vec{a}-7\vec{b}  

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