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  • Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 16 Maths.

Explain Solution RD Sharma Class 12 Chapter Algebra of Vectors Exercise 22.6 Question 16 Maths.

Answers (1)

Answer:

\frac{3}{\sqrt{22}} \hat{\imath}-\frac{3}{\sqrt{22}} \hat{\jmath}+\frac{2}{\sqrt{22}} \hat{k}

Hint:

Use vector of a line  \mathrm{AB}=\frac{A \vec{B}}{|A \vec{B}|}

Given:

\vec{a}=(\hat{\imath}+\hat{\jmath}+\hat{k}), \vec{b}=(2 \hat{\imath}-\hat{\jmath}+3 \hat{k}), \vec{c}=(\hat{\imath}-2 \hat{\jmath}+\hat{k})

Solution:

\begin{aligned} &\text { Let } \vec{d}=2 \vec{a}-\vec{b}+3 \vec{c} \\\\ &=2(\hat{\imath}+\hat{\jmath}+\hat{k})+(2 \hat{\imath}-\hat{\jmath}+3 \hat{k})+3(\hat{\imath}-2 \hat{\jmath}+\hat{k}) \\\\ &=3 \hat{\imath}-3 \hat{\jmath}+2 \hat{k} \end{aligned}
 

\begin{aligned} &|\vec{d}|=\sqrt{(3)^{2}+(3)^{2}+(2)^{2}}=\sqrt{22} \\\\ &\hat{d}=\frac{\vec{d}}{|\vec{d}|} \Rightarrow \hat{d}=\frac{3 \hat{\imath}-3 \hat{\jmath}+2 \hat{k}}{\sqrt{22}} \end{aligned}

\hat{d}=\frac{3}{\sqrt{22}} \hat{\imath}-\frac{3}{\sqrt{22}} \hat{\jmath}+\frac{2}{\sqrt{22}} \hat{k}

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