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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise very Short Answer type Question 49 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise very Short Answer type Question 49 Maths Textbook Solution.

Answers (1)

Answer: 6\hat{i}-9\hat{j}+18\hat{k}

Hint: You must know the rules of vector functions

Given: Find vector in direction of 2\hat{i}-3\hat{j}+6\hat{k}having magnitude 21 units

Solution: Let \vec{a}=2\hat{i}-3\hat{j}+6\hat{k}

      Unit vector

\begin{aligned} &\frac{\vec{a}}{|\vec{a}|}=\frac{(2 \hat{i}-3 \hat{j}+6 \hat{k})}{\sqrt{2^{2}+(-3)^{2}+(6)^{2}}}\\ \end{aligned}

\begin{aligned} &=\frac{(2 \hat{i}-3 \hat{j}+6 \hat{k})}{\sqrt{49}}\\ \end{aligned}

\begin{aligned} &=\frac{(2 \hat{i}-3 \hat{j}+6 \hat{k})}{7}\\ \end{aligned}

We know, magnitude is 21 units

\begin{aligned} &|\vec{a}|=21\\ \end{aligned}

\begin{aligned} &\frac{\vec{a}}{21}=\frac{1}{7}(2 \hat{i}-3 \hat{j}+6 \hat{k})\\ \end{aligned}

\begin{aligned} &\vec{a}=3(2 \hat{i}-3 \hat{j}+6 \hat{k})\\ \end{aligned}

\begin{aligned} &=6 \hat{i}-9 \hat{j}+18 \hat{k} \end{aligned}

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