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  • Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 6

Provide solution for RD Sharma maths class 12 chapter 22 Algebra of Vectors exercise Fill in the blanks question 6

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

Hint:-To solve this equation we use \hat{A}=\frac{\vec{A}}{|\vec{A}|}

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

Solution:-  we have Vector of magnitude 21 units in the direction of the vector 3 \hat{i}-6 \hat{j}+2 \hat{k}

\begin{aligned} &=\frac{3 \hat{i}-6 \hat{j}+2 \hat{k}}{\sqrt{9+36+4}} \\\\ &\hat{A}=\frac{3 \hat{i}-6 \hat{j}+2 \hat{k}}{\sqrt{49}} \end{aligned}

\begin{aligned} &\hat{A}=\frac{3 \hat{i}}{7}-\frac{6 \hat{j}}{7}+\frac{2 \hat{k}}{7} \\\\ &\vec{B}=|B| \hat{A} \end{aligned}

\begin{aligned} &\vec{B}=21\left[\frac{3 \hat{i}}{7}-\frac{6 \hat{j}}{7}+\frac{2 \hat{k}}{7}\right] \\\\ &\vec{B}=9 \hat{i}-18 \hat{j}+6 \hat{k} \end{aligned}

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