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  • Find the position vector of a point R which divides the line joining two points P and Q whose position vectors  are  and   respectively, in the ratio 2 : 1  externally

Q.15 (2)   Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are \hat i + 2 \hat j - \hat k and  - \hat i + \hat j + \hat krespectively, in the ratio 2 : 1 externally

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best_answer

As we know 

The position vector of the point R which divides the line segment PQ in ratio m:n externally:

\vec r=\frac{m\vec b-n\vec a}{m-n}

Here 

position vector os P = \vec a = i + 2 j - k

the position vector of Q  = \vec b=- i + j + k

m:n = 2:1

And Hence

\vec r = \frac{2(-\hat i+\hat j +\hat k)-1(\hat i+2\hat j-\hat k)}{2-1}=\frac{-2\hat i+2\hat j +2\hat k-\hat i-2\hat j+\hat k}{1}

\vec r = -3\hat i +3\hat k

 

Posted by

Pankaj Sanodiya

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