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  • Provide Solution For R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise Very Short Answer Type Question 24 Maths Textbook Solution.

Provide Solution For  R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise Very Short Answer Type  Question 24 Maths Textbook Solution.

Answers (1)

Answer: \frac{1}{\sqrt{41}}\left ( 3\hat{i}+4\hat{j}-4\hat{k} \right )

Hint: You must know the rules of vector functions

Given: \vec{a}=\hat{i}+2\hat{j},\vec{b}=\hat{j}+2\hat{k}, find unit vector 3\vec{a}-2\vec{b}

Solution: \vec{a}=\hat{i}+2\hat{j},\vec{b}=\hat{j}+2\hat{k}

Hence,

\begin{aligned} &3 \vec{a}-2 \vec{b}=3(\hat{i}+2 \hat{j})-2(\hat{j}+2 \hat{k}) \\ &=3 \hat{i}+6 \hat{j}-2 \hat{j}-4 \hat{k} \\ &=3 \hat{i}+4 \hat{j}-4 \hat{k} \end{aligned}

Hence, unit vector along,

\begin{aligned} &3 \vec{a}-2 \vec{b}=\frac{3 \hat{i}+4 \hat{j}-4 \hat{k}}{\sqrt{(3)^{2}+(4)^{2}+(-4)^{2}}} \\ &=\frac{3 \hat{i}+4 \hat{j}-4 \hat{k}}{\sqrt{9+16+16}} \\ &=\frac{1}{\sqrt{41}}(3 \hat{i}+4 \hat{j}-4 \hat{k}) \end{aligned}

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