RD Sharma Solutions Class 12 Straight Line In Space Exercise 28.5

RD Sharma Solutions for Class 12 Maths Chapter 28 Straight Line in Space Exercise 28.5, is provided here for students prepare well for their board exams. Tutors have designed the solutions in a unique and simple method where any student can grasp the topics clearly. The RD Sharma Solutions to this chapter are readily available in the pdf format, which can be downloaded by the students easily from the links provided below and can start practising offline to score good marks in their board exams.

Download PDF of Rd Sharma Solution for Class 12 Maths Chapter 28 Exercise 5

rd sharma class 12 solution for maths chapter 28 ex 5 1
rd sharma class 12 solution for maths chapter 28 ex 5 2
rd sharma class 12 solution for maths chapter 28 ex 5 3
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rd sharma class 12 solution for maths chapter 28 ex 5 5
rd sharma class 12 solution for maths chapter 28 ex 5 6

 

Access Answers for Rd Sharma Solution Class 12 Maths Chapter 28 Exercise 5

Q1.i

Solution:

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 56

Let us solve for b, we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 57……… (3)

By solving (2) and (3), we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 58

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 59

Now let us substitute the above obtained values in equation (1), to get the shortest distance between given lines,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 60

Hence, the shortest distance is 3√30 units.

ii.

Solution:

Given:

Equation of lines is,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 61

We know that,

Shortest distance between lines
RD Sharma Solutions for Class 12 Maths Chapter 28 – image 62is given by

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 63…….. (1)

Where,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 64

So now,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 65……. (2)

Let us solve for b, we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 66…… (3)

By solving (2) and (3), we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 67

= -512

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 68

Now let us substitute the above obtained values in equation (1), to get the shortest distance between given lines,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 69

Hence, the shortest distance is 512/√3968 units.

iii.

Solution:

Given:

Equation of lines is,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 70

We know that,

Shortest distance between lines
RD Sharma Solutions for Class 12 Maths Chapter 28 – image 71is given by

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 72…….. (1)

Where,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 73

So now,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 74…….. (2)

Let us solve for b, we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 75……… (3)

By solving (2) and (3), we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 76

= 1

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 77

Now let us substitute the above obtained values in equation (1), to get the shortest distance between given lines,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 78

Hence, the shortest distance is 1/√6 units.

iv.

Solution:

Given:

The vector equations are

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 79

The above equations can be written as

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 80

By using the formula,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 81

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 82

Hence,

The shortest distance is 9/3√2 = 3/√2 units.

v.

Solution:

Given:

Equation of lines is,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 83

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 84

We know that,

Shortest distance between lines
RD Sharma Solutions for Class 12 Maths Chapter 28 – image 85is given by

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 86…….. (1)

Where,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 87

So now,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 88……. (2)

Let us solve for b, we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 89

By solving (2) and (3), we get

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 90

= 15

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 91

Now let us substitute the above obtained values in equation (1), to get the shortest distance between given lines,

RD Sharma Solutions for Class 12 Maths Chapter 28 – image 92

Hence, the shortest distance is 5/√2 units.

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