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Find the position vector of the mid point of the vector joining the points $P(2, 3, 4)$ and $Q(4, 1, –2)$.

$\begin{array}{1 1}(A) 3\hat i + 2\hat j - \hat k. \\ (B) 3\hat i + 2\hat j + \hat k. \\(C) 6\hat i + 4\hat j -2 \hat k. \\(D) 6\hat i + 4\hat j +2 \hat k. \end{array} $

1 Answer

  • Mid point formula $\overrightarrow{OR}=\large\frac{\overrightarrow{OP}+\overrightarrow{OQ}}{1+1}$
Step 1:
Let $\overrightarrow{OP}=2\hat i+3\hat j+4\hat k$
$\;\;\;\overrightarrow{OQ}=4\hat i+\hat j-2\hat k$
Since it is given that $\overrightarrow{R}$ divides $\overrightarrow{PQ}$ into two equal halves,we can use mid point formula here.
Step 2:
Mid point formula $\overrightarrow{OR}=\large\frac{\overrightarrow{OP}+\overrightarrow{OQ}}{1+1}$
$\qquad\qquad\qquad\qquad=\large\frac{(2\hat i+3\hat j+4\hat k)+(4\hat i+\hat j-2\hat k)}{2}$
$\qquad\qquad\qquad\qquad=\large\frac{(6\hat i+4\hat j+2\hat k)}{2}$
$\qquad\qquad\qquad\qquad=2\times\large\frac{(3\hat i+2\hat j+\hat k)}{2}$
$\qquad\qquad\qquad\qquad=3\hat i+2\hat j+\hat k$
$\overrightarrow{OR}=3\hat i+2\hat j+\hat k$
answered May 17, 2013 by sreemathi.v

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