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  • Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products Exercise 23.1 Question 2 Sub Question 2 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products  Exercise 23.1 Question 2 Sub Question 2 Maths Textbook Solution.

Answers (1)

Answer:    \lambda =\frac{16}{5}

Hints: if dot products of two vector are equal to zero then vectors are perpendicular to each other

Given:  \vec{a}=\lambda \hat{i}+2\hat{j}+\hat{k} and \vec{b}=5\hat{i}-9\hat{j}+2\hat{k}

Solution:

\vec{a}=\lambda \hat{i}+2\hat{j}+\hat{k}

\vec{b}=5\hat{i}-9\hat{j}+2\hat{k}

If \vec{a}.\vec{b}=0, them both \vec{a} and \vec{b} are \perp to each other

\begin{gathered} \Rightarrow \vec{a} \cdot \vec{b}=(\lambda \hat{\imath}+2 \hat{\jmath}+\widehat{k})(5 \hat{\imath}-9 \hat{\jmath}+2 \hat{k})=0 \\ \end{gathered}

                                                                                                                                                                         \left|\begin{array}{l} \hat{i} \cdot \hat{l}=1 \\ \hat{\imath} \cdot \hat{\jmath}=0 \end{array}\right|

5\lambda -18+2=0

5\lambda -16=0

5\lambda =16

\lambda =\frac{16}{5}

 

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