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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 i + 2 j − k and – i + j + k respectively, in the ratio 2 : 1 internally

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

Answers (1)

best_answer

As we know 

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

\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}{3}

\vec r = \frac{-2\hat i+2\hat j +2\hat k+\hat i+2\hat j-\hat k}{3}=\frac{-\hat i+4\hat j+\hat k}{3}

\vec r = \frac{-\hat i}{3}+\frac{4\hat j}{3}+\frac{\hat k}{3}

 

Posted by

Pankaj Sanodiya

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