# Need solution for RD Sharma maths Class 12 Chapter 28 The Plane Exercise 28.9 Question 6 textbook solution.

Answer : The answer of the given question are $x-2 y+2 z+2=0, x-2 y+2 z-4=0$

Hint :

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

Given :

$x-2 y+2 z-3=0 \text {, Point }(1,1,1)$

Solution :

Since the planes are parallel to  $x-2 y+2 z-3=0$ they must be of the form $x-2 y+2 z+\theta=0$

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

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

According to the question, the distance of the plane from  $(1,1,1)$ is 1 Unit

\begin{aligned} &\left|\frac{1 \times 1+(-2) \times 1+2 \times 1+\theta}{\sqrt{1^{2}+(-2)^{2}+2^{2}}}\right|=1 \\ &\left|\frac{1+\theta}{3}\right|=1 \end{aligned}

\begin{aligned} &\frac{1+\theta}{3}=1 \text { Or } \frac{1+\theta}{3}=-1 \\ &\theta=2 \text { Or }-4 \end{aligned}

The required planes are

$x-2 y+2 z+2=0 \& x-2 y+2 z-4=0$

## Related Chapters

### Preparation Products

##### Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
##### Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
##### NEET Foundation + Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 54999/- ₹ 42499/-
##### NEET Foundation + Knockout NEET 2024 (Easy Installment)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 3999/-