RD Sharma Books are the teacher's favorite, and if a student understands and learns from the concepts from this book. The RD Sharma Class 12th Exercise 28.15 solutions are crafted by subject experts who provide easy methods to solve every question. This particular exercise has 15 questions to clarify the concept in a better way.
Also Read - RD Sharma Solutions For Class 9 to 12 Maths
This chapter, 'The Plane,' discusses 2D surfaces having infinite dimensions with no thickness such that when two lines join them, both of them lie on the surface entirely and find the shortest distance between them.
The Plane exercise 28.15 question 1
Answer: $\left(-\frac{6}{61}, \frac{-8}{61}, \frac{12}{61}\right)$The Plane exercise 28.15 question 2
Answer: $\left(\frac{73}{25},-\frac{6}{5}, \frac{39}{25}\right)$The Plane exercise 28.15 question 3
Answer: $(1,6,0), 2 \sqrt{6}$The Plane exercise 28.15 question 4
Answer: $(1,2,1), 2 i+\frac{3}{2} \hat{\jmath}+\frac{3}{2} \hat{k}$$Q(1,2,1)$
Solution:
$\begin{aligned} &\vec{r}=x \hat{\imath}+y \hat{\jmath}+z \hat{k} \\\\ &2 x-y+z=4 \\\\ &\frac{x-3}{2}=\frac{y-1}{-1}=\frac{z-2}{1} \end{aligned}$
$\begin{aligned} &=\frac{-2(6-1+2-4)}{(4+1+1)} \\\\ &=\frac{-2(3)}{6} \\\\ &=-1 \end{aligned}$
$\begin{aligned} &\frac{x-3}{2}=-1 \\\\ &\frac{y-1}{-1}=-1 \\\\ &\frac{z-2}{1}=1\\ \end{aligned}$
$\begin{aligned} &x=1 \\ &y=2 \\ &z=1 \end{aligned}$
Point$(1,2,1)$
Passing $(3,1,2),$ the point.
direction $\rightarrow 2,-1,1$
$\begin{aligned} &\frac{x-3}{2}=\frac{y-1}{-1}=\frac{z-2}{1} \\\\ &\Rightarrow \vec{r}=3 \hat{\imath}+\hat{\jmath}+2 \hat{k} \\\\ &(2 \hat{\imath}+-\hat{\jmath}+\hat{k}) \end{aligned}$
point $(3,1,2)$
point $q=(1,2,1)$
So the middle point $=2+\frac{3}{2}+\frac{3}{2}$
i.e, $2 i+\frac{3}{2} \hat{\jmath}+\frac{3}{2} k$
The Plane exercise 28.15 question 5
Answer: $\left(-\frac{1}{12}, \frac{25}{12},-\frac{1}{6}\right), \frac{13}{\sqrt{24}}$The Plane exercise 28.15 question 6
Answer:$1$The Plane exercise 28.15 question 7
Answer: $(5.2,6) ; \sqrt{11}$The Plane exercise 28.15 question 8
Answer: $(-3,5,2)$The Plane exercise 28.15 question 9
Answer:$13$The Plane exercise 28.15 question 10
Answer: $\frac{13}{12} \sqrt{6},\left(-\frac{1}{12}, \frac{25}{12},-\frac{2}{12}\right)$The Plane exercise 28.15 question 11
Answer:$(7,0,3)(-1,4,-1), \sqrt{6}$The Plane exercise 28.15 question 13
Answer:$\frac{12}{29}, \frac{-18}{29}, \frac{24}{29}$The Plane exercise 28.15 question 14
Answer:$\left(0, \frac{5}{2}, 0\right) ; \sqrt{6}$The Plane exercise 28.15 question 15
Answer:$\left(3, \frac{7}{2}, \frac{11}{2}\right),(4,4,7)$RD Sharma Chapter-wise Solutions
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