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  • Please solve RD Sharma class 12 chapter The Plane exercise 28.8 question 17 maths textbook solution

Please solve RD Sharma class 12 chapter The Plane exercise 28.8 question 17 maths textbook solution

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Answer:-  The answer of the given question is x+y+z=a+b+c.

Hints:-  By substituting \vec{r}=x \hat{\imath}+y \hat{j}+z \hat{k} in equation (ii)

Given:-  (a, b, c) and parallel to plane \vec{r} \cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=2                 

Solution:-  Any plane passes through the point (a, b, c) and parallel to plane \vec{r} \cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=2 is given by

        \vec{r} \cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=\lambda…(i)

Here, the position vector \vec{r} of this point is \vec{r}=a \hat{\imath}+b \hat{\jmath}+c \hat{k}

∴ Equation (i) becomes        

        \begin{gathered} (a \hat{\imath}+b \hat{\jmath}+c \hat{k}) \cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=\lambda \\\\ \Rightarrow a+b+c=\lambda \end{gathered}

Substituting \lambda =a+b+c in equation (i), we obtain

        \vec{r} \cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=a+b+c         … (ii)

This is vector equation of the required plane

Substituting \vec{r}=x \hat{\imath}+y \hat{\jmath}+z \hat{k} in equation (ii)


        \begin{gathered} (x \hat{\imath}+y \hat{\jmath}+z \hat{k}) \cdot(\hat{\imath}+\hat{\jmath}+\hat{k})=a+b+c \\\\ x+y+z=a+b+c \end{gathered}

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