Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Vector Algebra
0 votes

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} $

Can you answer this question?

1 Answer

0 votes
  • 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

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App