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  • Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28 point 6 question 4 sub question 1 maths textbook solution

Need solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 4 sub question 1 maths textbook solution

Answers (1)

Answer:

              \lambda =17

Hint:

              \cos \theta=\frac{\vec{n}_{1} \cdot \vec{n}_{2}}{\left|\vec{n}_{1}\right| \cdot \vec{n}_{2} \mid}=0

Given:

              \overrightarrow{\boldsymbol{r}} \cdot(\hat{\boldsymbol{\imath}}+2 \hat{\boldsymbol{\jmath}}+3 \hat{\boldsymbol{k}})=7 \text { And } \vec{r} \cdot(\lambda \hat{\imath}+2 \hat{\jmath}-7 \hat{k})=26

Solution:

Here

\begin{aligned} &\vec{n}_{1}=\hat{\imath}+2 \hat{\jmath}+3 \hat{k}, \text { on comparing wit } \overrightarrow{\boldsymbol{r}} \cdot(\hat{\boldsymbol{\imath}}+2 \hat{\boldsymbol{j}}+3 \widehat{\boldsymbol{k}})=\mathbf{7}\\ &\vec{n}_{2}=\lambda \hat{\imath}+2 \hat{\jmath}-7 \hat{k}, \text { on comparing with } \vec{r} \cdot(\lambda \hat{\imath}+2 \hat{\jmath}-7 \hat{k})=26\\ &\vec{n}_{1} \cdot \vec{n}_{2}=0 \quad\left[\because\left|\vec{n}_{1}\right| \cdot\left|\vec{n}_{2}\right| \neq 0\right]\\ &(\hat{\imath}+2 \hat{\jmath}+3 \hat{k}) \cdot(\lambda \hat{\imath}+2 \hat{\jmath}-7 \hat{k})=0\\ &\lambda+4-21=0\\ &\lambda=17 \end{aligned}

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