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  • Write the operation vector of the point which divides the join of points with position vectors and

Write the operation vector of the point which divides the join of points with position vectors 3\vec{a}-2\vec{b} and 2\vec{a}+3\vec{b} in the ratio 2:1.

 

 

 

 
 
 
 
 

Answers (1)

Let A and B be the given points with position vector 3\vec{a}-2\vec{b} and 2\vec{a}+3\vec{b} respectively.
Let P and Q be the points dividing AB in the ratio 2:1 internally and externally respectively then.
Position vector P= \frac{1 \left ( 3\vec{a}-2\vec{b} \right )+2\left ( 2\vec{a} +3\vec{b}\right )}{1+2}
                             = \frac{7\vec{a}}{3}+\frac{4\vec{b}}{3}
Position vector of Q= \frac{1 \left ( 3\vec{a}-2\vec{b} \right )-2\left ( 2\vec{a} +3\vec{b}\right )}{1-2}
                                  = \vec{a}+8\vec{b}

Posted by

Ravindra Pindel

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