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Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise very Short Answer type Question 48 Maths Textbook Solution.

Answers (1)

Answer: \frac{1}{7}\left ( 3\hat{i}+2\hat{j}+6\hat{k} \right )

Hint: You must know the rules of vector functions

Given: Find a unit vector in direction of \vec{PQ} when P\left ( 1,3,0 \right ) &Q\left ( 4,5,6 \right )

Solution: P\left ( 1,3,0 \right ) & Q\left ( 4,5,6 \right )

\begin{aligned} &\therefore \overrightarrow{P Q}=(4 \hat{i}+5 \hat{j}+6 \hat{k})-(\hat{i}+3 \hat{j}+0 \hat{k}) \\ &=4 \hat{i}+5 \hat{j}+6 \hat{k}-\hat{i}-3 \hat{j}-0 \hat{k} \\ &\overrightarrow{P Q}=3 \hat{i}+2 \hat{j}+6 \hat{k} \\ &|\overrightarrow{P Q}|=\sqrt{(3)^{2}+(2)^{2}+(6)^{2}} \\ &=\sqrt{9+4+36} \\ &=\sqrt{49} \\ &=7 \\ \end{aligned}

Unit Vector:

\begin{aligned} &\frac{\overline{P Q}}{|\overline{P Q}|}=\frac{1}{7}(3 \hat{i}+2 \hat{j}+6 \hat{k}) \end{aligned}

 

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