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  • Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.6 Question 12 Maths Textbook Solution.

Please Solve RD Sharma Class 12 Chapter 22 Algebra of Vectors Exercise 22.6 Question 12 Maths Textbook Solution.

Answers (1)

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Answer:

\frac{1}{\sqrt{3}}(\hat{\imath}+\hat{\jmath}+\hat{k})

Hint:

Unit vector  =\frac{P \vec{Q}}{|P \vec{Q}|}

Given:

P and Q are the points  (1,2,3) \text { and }(4,5,6)

Solution:

\begin{aligned} P \vec{Q} &=\vec{Q}-\vec{P} \\ &=(4 \hat{i}+5 \hat{\jmath}+6 \hat{k})-(\hat{\imath}+2 \hat{\jmath}+3 \hat{k}) \\ P \vec{Q} &=((3 \hat{\imath}+3 \hat{\jmath}+3 \hat{k})) \end{aligned}

Any unit vector on the direction of  P \vec{Q} is

\begin{aligned} &\frac{P \vec{Q}}{|P \vec{Q}|}=\frac{3 \hat{\imath}+3 \hat{\jmath}+3 \hat{k}}{\sqrt{3^{2}+3^{2}+3^{2}}}=\frac{(3,3,3)}{\sqrt{27}} \\ &=\frac{3 \hat{\imath}+3 \hat{\jmath}+3 \hat{k}}{3 \sqrt{3}} \\ &=\frac{\hat{\imath}+\hat{\jmath}+\hat{k}}{\sqrt{3}} \end{aligned}

Required unit vector =\frac{1}{\sqrt{3}}(\hat{\imath}+\hat{\jmath}+\hat{k})

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