Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • School
  • Need solution for RD Sharma maths class 12 chapter The Plane exercise 28.15 question 15

Need solution for RD Sharma maths class 12 chapter The Plane exercise 28.15 question 15

Answers (1)

Answer: \left(3, \frac{7}{2}, \frac{11}{2}\right),(4,4,7)

Hint:

Distance \rightarrow \sqrt{\left(x_{1}-x_{2}\right)^{2}+\left(y_{1}-y_{2}\right)^{2}+\left(z_{1}-z_{2}\right)^{2}}

\vec{d}=\vec{r} \cdot \vec{n}

                            

Given:

Find the position vector of the foot of the perpendicular and the perpendicular distance from the point P with position vector 2 \tilde{i}+3 \hat{\jmath}+4 \hat{k}  to the plane  \vec{r} \cdot(\hat{\imath}+\hat{\jmath}+3 \hat{k})-26=0 . Also find the image of P in the plane

Solution:

\begin{aligned} &\frac{x-2}{2}=\frac{y-3}{1}=\frac{z-4}{3}=t \\\\ &x=2+2 t \\\\ &y=3+t \\\\ &z=4+3 t \end{aligned}

\begin{aligned} &\Rightarrow[(2+2 t) \hat{i}+(3+t) \hat{j}+(4+3 t) \hat{k}][2 \hat{i}+\hat{j}+3 \hat{k}]=26 \\\\ &\Rightarrow 19+14 t=26 \\\\ &t=\frac{1}{2} \end{aligned}

Putting the value of t in equation 1
i.e,

\begin{aligned} & x=3, \\\\ &y=\frac{7}{2}, \\\\ &z=\frac{11}{2} \end{aligned}

\mathrm{PQ} \Rightarrow(3-2)^{2}+\left(\frac{7}{2}-3\right)^{2}+\left(\frac{11}{2}-2\right)^{2}

        \begin{aligned} &=\sqrt{1+\left(\frac{1}{2}\right)^{2}+\left(\frac{11}{2}\right)^{2}}, \\\\ &=\sqrt{1+\frac{1}{4}+\frac{9}{4}} \end{aligned}

        \begin{aligned} &=\sqrt{\frac{14}{4}} \\\\ &=\frac{\sqrt{14}}{2} \end{aligned}

Image ,

x=2+2(1)=4

\begin{aligned} &y=3+1=4 \\\\ &z=4+3(1)=7 \end{aligned}

Image (4,4,7) Ans
Foot \left(3, \frac{7}{2}, \frac{11}{2}\right) Ans


 

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 Class 10, 12 board exams 2025 from April 7 to 11 for sports students
anam-khan

CBSE Class 12 history paper 2025 moderately difficult, tested students’ understanding
anam-khan

CBSE Class 12 Computer Science Exam Analysis 2025: Paper 'moderate', but 'tougher' than last three years

Latest Question