Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Explain solution RD Sharma class 12 chapter 28 The Plane exercise very short answer type question 24 maths

Explain solution RD Sharma class 12 chapter 28 The Plane exercise very short answer type question 24 maths

Answers (1)

Answer:

cos^{-1}\frac{11}{21}

Hint:

 cos\theta =\frac{\left | \overrightarrow{n_1}\overrightarrow{n_2} \right |}{\left | \overrightarrow{n_1} \right |.\left | \overrightarrow{n_2} \right |}

Given:

 \overrightarrow{r}.(\widehat{i}-2\widehat{j}-2\widehat{k})=1 \text { and }\overrightarrow{r}.(3\widehat{i}-6\widehat{j}+2\widehat{k})=0

Solution:

\overrightarrow{r}.(\widehat{i}-2\widehat{j}-2\widehat{k})=1 \qquad \qquad \dots(i)

So the vector, normal to the plane is

\overrightarrow{n_1}=(\widehat{i}-2\widehat{j}-2\widehat{k})

\overrightarrow{r}.(3\widehat{i}-6\widehat{j}+2\widehat{k})=0 \qquad \qquad \dots (ii)

So the vector, normal to the plane is

\overrightarrow{n_2}=(3\widehat{i}-6\widehat{j}+2\widehat{k})

Angle between (i) & (ii)

\begin{aligned} &\Rightarrow cos\theta =\frac{\left | \overrightarrow{n_1}\overrightarrow{n_2} \right |}{\left | \overrightarrow{n_1} \right |.\left | \overrightarrow{n_2} \right |}\\ &\Rightarrow cos\theta = \frac{\left | (\widehat{i}-2\widehat{j}-2\widehat{k}).(3\widehat{i}-6\widehat{j}+2\widehat{k}) \right |}{\left | (\widehat{i}-2\widehat{j}-2\widehat{k}) \right |\left | (3\widehat{i}-6\widehat{j}+2\widehat{k}) \right |}\\ &\Rightarrow cos\theta =\frac{3+12-4}{\sqrt{1+4+4}.\sqrt{9+36+4}}\\ &\Rightarrow cos\theta =\frac{11}{3\times 7}\\ &\Rightarrow cos\theta =\frac{11}{21}\\ &\Rightarrow \theta =cos^{-1}\frac{11}{21} \end{aligned}

Posted by

Gurleen Kaur

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 Class 12 result verification 2024 application out at cbse.gov.in; last date, fees
anam-khan

CBSE results 2024 later for 102 students over fake certificates; board issues show cause notice
anam-khan

What after CBSE Class 12 results 2024? From CUET UG to JEE Advanced, all you need to know

Latest Question