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  • Need solution for RD Sharma Maths Class 12 Chapter 22 Algera of Vectors Excercise 22.6 Question 14

Need solution for RD Sharma Maths Class 12 Chapter 22 Algera of Vectors Excercise 22.6 Question 14

Answers (1)

Answer:

(3,2,1)

Hint:

Mid – point  =\frac{ \vec{OP}+ \vec{OQ}}{2}

Given:

The points are  P(2,3,4) \text { and } Q(4,1,-2)

Solution:

\begin{aligned} &O \vec{P}=2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k} \\ &\vec{OQ}=4 \hat{\imath}+\hat{\jmath}-2 \hat{k} \end{aligned}

Let R the mid - point of the line joining the point P and Q.

\begin{aligned} &\therefore O \vec{R}=\frac{O \vec{P}+O \vec{Q}}{2} \\ &=\frac{(2 \hat{\imath}+3 \hat{\jmath}+4 \hat{k})+(4 \hat{\imath}+\hat{\jmath}-2 \hat{k})}{2} \end{aligned}
\begin{aligned} &=\frac{6 \hat{\imath}+4 \hat{j}+2 \hat{k}}{2} \\ &=3 \hat{i}+2 \hat{j}+\hat{k} \end{aligned}

∴The mid – point are  \left ( 3,2,1 \right )

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