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  • Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28 point 6 question 13 maths textbook solution

Explain solution for RD Sharma maths class 12 chapter 28 The Plane exercise 28.6 question 13 maths textbook solution

Answers (1)

Answer:

              Therefore, required equation of the plane is x+y+z=a+b+c

Hint:

              Using properties of plane

Given:

              Points \left ( a,b,c \right ) and plane \overrightarrow{r}\cdot \left ( \hat{i}+\hat{j}+\hat{k} \right )=2

Solution:

The required plane is parallel to the plane \overrightarrow{r}\cdot \left ( \hat{i}+\hat{j}+\hat{k} \right )=2

Any plane parallel to \overrightarrow{r}\cdot \left ( \hat{i}+\hat{j}+\hat{k} \right )=2 is given as \overrightarrow{r}\cdot \left ( \hat{i}+\hat{j}+\hat{k} \right )=k

Further, it is given that the plane is passing through \left ( a,b,c \right ). So point \left ( a,b,c \right )should satisfy the equation of the plane

We have \left ( a\hat{i}+b\hat{j}+c\hat{k} \right )\cdot \left (\hat{i}+\hat{j}+\hat{k} \right )=k

                                                 a+b+c=k

Hence, the equation of the required plane is,

                                                \overrightarrow{r}\cdot \left ( \hat{i}+\hat{j}+\hat{k} \right )= a+b+c

Or, x+y+z= a+b+c

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