RD Sharma Solutions Class 12 The Plane Exercise 29.3

RD Sharma Solutions for Class 12 Maths Chapter 29 The Plane Exercise 29.3, is provided here. Our solution module utilizes various shortcut tips and practical examples to explain all the exercise questions in a simple and easily understandable language and to help students grasp the concepts faster and to make learning fun. The RD Sharma Solutions to this exercise are provided in pdf format, which can be downloaded easily from the links provided below.

Download PDF of RD Sharma Solutions For Class 12 Maths Chapter 29 Exercise 3

 

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Access RD Sharma Solutions For Class 12 Maths Chapter 29 Exercise 3

EXERCISE 29.3

Q1.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 24

Q2. i

Solution:

Given:

The vector equation of plane is

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 25

12x – 3y + 4z + 5 = 0

Hence, the Cartesian form of the equation of the plane is 12x – 3y + 4z + 5 = 0.

ii.

Solution:

Given:

The equation of plane is:

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 26

-x + y + 2z = 9

Hence, the Cartesian form of the equation of the plane is -x + y + 2z = 9.

Q3.

Solution:

Given:

For xy-plane,

This plane is passing through the origin and is perpendicular to z-axis.

So,

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 27

For xz-plane,

It passes through origin and perpendicular to y-axis,

So,

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 28

For yz-plane,

It passes through origin and perpendicular to x-axis,

So,

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 29

Hence, equation of xy, yz and xz-plane is given by

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 30

Q4.i.

Solution:

Given:

The equation of plane is:

2x – y + 2z = 8

By putting the values, we get

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 31

ii.

Solution:

Given:

The Cartesian equation of plane is:

x + y – z = 5

By putting the values, we get

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 32

iii.

Solution:

Given:

The Cartesian equation of plane is:

x + y = 3

By putting the values, we get

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 33

Q5.

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 34

The given plane is passing through the point (1, -1, 1) and normal to the line joining A(1, 2, 5) and B(-1, 3, 1).

So,

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 35

Now, multiply by (-1) on both sides

So,

RD Sharma Solutions for Class 12 Maths Chapter 29 - image 36

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