# Need solution for RD Sharma maths Class 12 Chapter 28 The Plane Exercise 28.9 Question 8 textbook solution.

Answer : The answer of the given question is $\frac{9}{\sqrt{78}}$ unit

Hint :

$P=\left|\frac{a x_{1}+b y_{1}+c z_{1}+d}{\sqrt{a^{2}+b^{2}+c^{2}}}\right|$

Given :

Points : $A(3,3,3)$

Plane : $\vec{r} \cdot(5 \hat{i}+2 \hat{j}-7 \hat{k})+9=0$, which in Cartesian form

Solution :

$5 x+2 y-7 z+9=0$ and point $(3,3,3)$

We know the distance of point $\left(x_{1}, y_{1}, z_{1}\right)$ from the plane

$p: a x+b y+c z+d=0$ Is given by

$P=\left|\frac{a x_{1}+b y_{1}+c z_{1}+d}{\sqrt{a^{2}+b^{2}+c^{2}}}\right|$

Putting the values

$P=\left|\frac{5 \times 3+2 \times 3+(-7) \times 3+9}{\sqrt{5^{2}+2^{2}+(-7)^{2}}}\right|=\frac{9}{\sqrt{78}} \text { Units }$

The distance of the point $(3,3,3)$ from the plane,

$\vec{r} \cdot(5 \hat{i}+2 \hat{j}-7 \hat{k})+9=0 \text { is } \frac{9}{\sqrt{78}} \text { Units }$

NO $No schools\sum \bigcup \Delta \Omega \binom{}{}^{\circ}$$No schools\sum \bigcup \Delta \Omega \binom{}{}^{\circ}$$No schools\sum \bigcup \Delta \Omega \binom{}{}^{\circ}$NO GOING TO SCHOOL

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