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 reminds schools to submit registration data of Class 9, 11 students by October 16
anam-khan

CBSE reopens online portal for submission of LOC for Class 10, 12 board exams 2026; submit forms by Oct 8
anam-khan

CBSE private candidates challenge cancellation of post-Class 12 additional subject exam in Delhi HC

Latest Question