Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Please solve RD Sharma class 12 chapter The Plane exercise 28.3 question 13 sub question (i) maths textbook solution

Please solve RD Sharma class 12 chapter The Plane exercise 28.3  question 13 sub question (i)  maths textbook solution

Answers (1)

best_answer

Answer:

The normal to the given pairs of planes are perpendicular to each other.

Hint:

\overrightarrow{n_{1}} \cdot \overrightarrow{n_{2}}=0

Given:
\begin{aligned} &x-y+z-2=0 \\ &3 x+2 y-z+4=0 \end{aligned}

Solution:

The vector equation of the planes x-y+z-2=0 can be written as
\begin{aligned} &(x \hat{\imath}+y \hat{\jmath}+z \hat{k})(\hat{\imath}-\hat{\jmath}+\hat{k})=2 \\ &\Rightarrow \vec{r} \cdot(\hat{\imath}-\hat{\jmath}+\hat{k})=2 \end{aligned}

The normal to this plane is \overrightarrow{n_{1}}=\hat{\imath}-\hat{\jmath}+\hat{k} \ldots(\mathrm{i})

The vector equation of the plane 3 x+2 y-z+4=0 can be written as
\begin{aligned} &(x \hat{\imath}+y \hat{\jmath}+z \hat{k})(3 \hat{\imath}+2 \hat{\jmath}-\hat{k})=-4 \\ &\Rightarrow \vec{r} \cdot(3 \hat{\imath}+2 \hat{\jmath}-\hat{k})=-4 \end{aligned}

The normal to this plane is

\overrightarrow{n_{2}}=3 \hat{\imath}+2 \hat{\jmath}-\hat{k} \ldots(ii)

Now,

\begin{aligned} &\overrightarrow{n_{1}} \cdot \overrightarrow{n_{2}}=(\hat{\imath}-\hat{\jmath}+\hat{k}) \cdot(3 \hat{\imath}+2 \hat{\jmath}-\hat{k}) \\ &\Rightarrow \overrightarrow{n_{1}} \cdot \overrightarrow{n_{2}}=(1)(3)+(-1)(2)+(1)(-1)=0 \end{aligned}

Hence \overrightarrow{n_{1}}  is perpendicular to \overrightarrow{n_{2}}

Therefore, the normal to the given pair of planes are perpendicular to each other.

Posted by

infoexpert26

View full answer

Crack CUET with india's "Best Teachers"

  • HD Video Lectures
  • Unlimited Mock Tests
  • Faculty Support
cuet_ads

Similar Questions

Trending Articles/News

anam-khan

CBSE date sheet 2025 for Classes 10, 12 likely in November last week: Reports
anam-khan

CBSE allows Class 10, 12 students from disaffiliated schools to appear for board exam 2025 from same school
anam-khan

CBSE withdraws affiliation of 21 schools, downgrades 6 schools in two states; most in Delhi

Latest Question