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  • Provide Solution For R.D. Sharma Maths Class 12 Chapter 23 Scalar or Dot Products Exercise 23.1 Question 15 Maths Textbook Solution.

Provide Solution For  R.D. Sharma Maths Class 12 Chapter 23 Scalar or Dot Products  Exercise 23.1 Question 15 Maths Textbook Solution.

Answers (1)

Answer: \lambda =-2

Hint: you must know the rules of solving vectors

Given: \begin{aligned} &\vec{a}=2 \hat{\imath}-\hat{\jmath}+\hat{k} \\ \end{aligned}                              Find \lambda

\begin{aligned} &\vec{b}=\hat{\imath}+\hat{\jmath}-2 \hat{k} \\ \end{aligned}                                        Such\: \: \vec{a} \: \: is \perp to \: \: \lambda \: \: \vec{b}+c

\begin{aligned} &\vec{c}=\hat{\imath}+3 \hat{\jmath}-\hat{k} \end{aligned}

Solution: The given vectors are  \begin{aligned} &\vec{a}=2 \hat{\imath}-\hat{\jmath}+\hat{k} \\ \end{aligned}

\begin{aligned} &\vec{b}=\hat{\imath}+\hat{\jmath}-2 \hat{k} \\ \end{aligned}  and \begin{aligned} &\vec{c}=\hat{\imath}+3 \hat{\jmath}-\hat{k} \end{aligned}

Now,

\begin{aligned} &\lambda \vec{b}+\vec{c}=\lambda(\hat{\imath}+\hat{\jmath}-2 \hat{k})+\hat{\imath}+3 \hat{\jmath}-\hat{k} \\ &=(\lambda+1) \hat{\imath}+(\lambda+3) \hat{\jmath}-(2 \lambda+1) \hat{k} \end{aligned}

It is given that

\begin{aligned} &\vec{a} \perp(\lambda \vec{b}+\vec{c}) \\\\ &\Rightarrow \vec{a}.(\lambda \vec{b}+\vec{c})=0 \\ \end{aligned}

\begin{aligned} &\Rightarrow 2(\lambda+1)-(\lambda+3)-(2 \lambda+1)=0 \\\\ &2 \lambda+2-\lambda-3-2 \lambda-1=0 \\\\ &\lambda=-2 \end{aligned}

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