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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise very Short Answer type Question 45 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise very Short Answer type Question 45 Maths Textbook Solution.

Answers (1)

Answer: \frac{4}{13}\hat{i}+\frac{3}{13}\hat{j}-\frac{12}{13}\hat{k}

Hint: You must know the rules of vector functions

Given: Find unit vector in direction of sum of vectors

\begin{aligned} &\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}, \\ &\vec{b}=2 \hat{i}+\hat{j}-7 \hat{k} \end{aligned}

Solution: We have,

\begin{aligned} &\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}, \\ &\vec{b}=2 \hat{i}+\hat{j}-7 \hat{k} \end{aligned}

Sum, \begin{aligned} &\vec{p}=\vec{a}+\vec{b}=2 \hat{i}+2 \hat{j}-5 \hat{k}+2 \hat{i}+\hat{j}-7 \hat{k} \\ \end{aligned}

\begin{aligned} &=4 \hat{i}+3 \hat{j}-12 \hat{k} \\ \end{aligned}

∴Required unit vector

\begin{aligned} &\frac{\vec{p}}{|\vec{p}|}=\frac{\vec{a}+\vec{b}}{|\vec{a}+\vec{b}|}=\frac{4 \hat{i}+3 \hat{j}-12 \hat{k}}{\sqrt{(4)^{2}+(3)^{2}+(-12)^{2}}} \\ &=\frac{4 \hat{i}+3 \hat{j}-12 \hat{k}}{\sqrt{16+9+144}} \\ &=\frac{4 \hat{i}+3 \hat{j}-12 \hat{k}}{\sqrt{169}} \\ &=\frac{4 \hat{i}+3 \hat{j}-12 \hat{k}}{13} \\ &\therefore \frac{4}{13} \hat{i}+\frac{3}{13} \hat{j}-\frac{12}{13} \hat{k} \end{aligned}

 

 

 

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