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  • Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors Exercise very Short Answer type Question 46 Maths Textbook Solution.

Need Solution for R.D.Sharma Maths Class 12 Chapter 22 Algebra of Vectors  Exercise very Short Answer type Question 46 Maths Textbook Solution.

Answers (1)

Answer: p=\frac{-1}{3}

Hint: You must know the rules of vector functions

Given: Find value of ‘p’

3\hat{i}+2\hat{j}+9\hat{k},\hat{i}-2\hat{pj}+3\hat{k} are parallel

Solution:

                  Let \vec{a}=3\hat{i}+2\hat{j}+9\hat{k}

\vec{b}=\hat{i}-2\hat{pj}+3\hat{k}

                                If \vec{a} &\vec{b} are parallel

\vec{b}=\lambda\vec{a}

\begin{aligned} &\hat{i}-2 \hat{p j}+3 \hat{k}=\lambda(3 \hat{i}+2 \hat{j}+9 \hat{k})\\ &\hat{i}-2 \hat{p j}+3 \hat{k}=3 \lambda \hat{i}+2 \lambda \hat{j}+9 \lambda \hat{k}\\ \end{aligned}

\therefore On comparing,

\begin{aligned} &3 \lambda=1 \Rightarrow \lambda=\frac{1}{3}\\ &3=9 \lambda \Rightarrow \lambda=\frac{1}{3}\\ \end{aligned}

\begin{aligned} &-2 p=2 \lambda \Rightarrow-2 p=2 \times \frac{1}{3} \Rightarrow p=\frac{-1}{3} \end{aligned}

 

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