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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.

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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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