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  • Provide solution for RD Sharma maths class 12 chapter The Plane exercise 28.8 question 2

Provide solution for RD Sharma maths class 12 chapter The Plane exercise 28.8 question 2

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Answer:-  The answer of the given question is \vec{r} \cdot(2 \hat{\imath}-3 \hat{\jmath}+5 \hat{k})+11=0

Hint:-  By putting the value of k in equation (ii)

Given:-  \vec{r} \cdot(2 \hat{\imath}-3 \hat{\jmath}+5 \hat{k})+2=0

Solution:-  Given equation of a plane is

        \vec{r} \cdot(2 \hat{\imath}-3 \hat{\jmath}+5 \hat{k})+2=0                          …(i)

We know that the equation of a plane parallel to given plane (i) is

        \vec{r} \cdot(2 \hat{\imath}-3 \hat{\jmath}+5 \hat{k})+k=0               … (ii)

As given that plane (ii) is passing through the point 3 \hat{\imath}+4 \hat{\jmath}-\hat{k} so it satisfy the equation (ii)

        \begin{aligned} &(3 \hat{\imath}+4 \hat{\jmath}-\hat{k}) \cdot(2 \hat{\imath}-3 \hat{\jmath}+5 \hat{k})+k=0 \\\\ &(3)(2)+(4)(-3)+(-1)(5)+k=0 \end{aligned}

                            k=11

Put the value of k in equation (ii)

        \vec{r} \cdot(2 \hat{\imath}-3 \hat{\jmath}+5 \hat{k})+11=0

So, the equation of the required plane is

        \vec{r} \cdot(2 \hat{\imath}-3 \hat{\jmath}+5 \hat{k})+11=0

 

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