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  • Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products Exercise 23.1 Question 2 Sub Question 3 Maths Textbook Solution.

Please Solve R.D.Sharma class 12 Chapter 23 Scaler or Dot Products  Exercise 23.1 Question 2 Sub Question 3 Maths Textbook Solution.

Answers (1)

Answer:    \lambda =3

Hints:  you must know the proper of vectors

Given: \vec{a}=2\hat{i}+3\hat{j}+4\hat{k} and \vec{b}=3\hat{i}+2\hat{j}-\lambda \hat{k}

Solution:\vec{a}=2\hat{i}+3\hat{j}+4\hat{k}

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

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

\begin{aligned} &\Rightarrow(2 \hat{\imath}+3 \hat{\jmath}+4 \widehat{k})(3 \hat{\imath}+2 \hat{\jmath}-\lambda \hat{k})=0 \\ &\Rightarrow 6+6-4 \lambda=0 \\ &12-4 \lambda=0 \\ &-4 \lambda=-12 \\ &\lambda=3 \end{aligned}                                      \left|\begin{array}{l} \hat{i} \cdot \hat{l}=1 \\ \hat{\imath} \cdot \hat{\jmath}=0 \end{array}\right|

                                                                                            

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