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  • please solve RD sharma class 12 chapter 28 The Plane exercise 28.8 question 2 maths textbook solution

please solve RD sharma class 12 chapter 28 The Plane exercise 28.8 question 2 maths textbook solution

Answers (1)

The answer of the given question is \vec{r}. \left (2\hat{i}-3\hat{j}+5k \right )+11=0

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

Given:-  \vec{r}.\left (2\hat{i}-3\hat{j}+5\hat{k} \right )+2=0

Solution:-  Given equation of a plane is

\vec{r}.\left (2\hat{i}-3\hat{j}+5\hat{k} \right )+2=0                                …(i)

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

\vec{r}.\left (2\hat{i}-3\hat{j}+5\hat{k} \right )+k=0                    … (ii)

As given that plane (ii) is passing through the point  3\hat{i}+4\hat{j}-\hat{k} so it satisfy the equation (ii)
(3\hat{i}+4\hat{j}-\hat{k}).(2\hat{i}-3\hat{j}+5\hat{k})+k=0\\ (3)(2)+(4)(-3)+(-1)(5)+k=0\\ k=11

Put the value of k in equation (ii)

\vec{r}.(2\hat{i}-3\hat{j}+5\hat{k})+11=0

So, the equation of the required plane is

\vec{r}.(2\hat{i}-3\hat{j}+5\hat{k})+11=0

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