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Edited By Lovekush kumar saini | Updated on Jan 25, 2022 09:48 AM IST

Class 12 students are stuck between completing the homework and preparing for their board exams. In mathematics, there are even possibilities to score grace marks for their steps in solving sums. But this is not the case in MCQs. The Multiple Choice Questions are easy as there are options provided, and this is why most of the students get confused while choosing the answer. RD Sharma solutions To help them prepare well to face these MCQs, the RD Sharma Class 12th Chapter 27 MCQ lends a helping hand.

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Straight Line in Space exercise Multiple choice question 1

Let θ be the angle between the given lines.

Now,

Hence,

So, the correct option is (d) 90°

Straight Line in Space exercise Multiple choice question 2

Thus the two lines are parallel to the vector and pass through the points and

Now,

Since the distance between the two parallel lines is 0, the given lines are coincident.

So, the correct option is (a) coincident.

Straight Line in Space exercise Multiple choice question 3

The given lines are parallel to the vectors

Vector perpendicular to the given two lines is

Hence, the direction ratios of the line perpendicular to the given two lines are proportional to

Straight Line in Space exercise Multiple choice question 4

The given lines are parallel to the vectors

Let θ be the angle between the given lines.

Now,

So, the correct option is

Straight Line in Space exercise Multiple choice question 5

From (1) and (2) we get,

Also,

So, the given equation can be re-written as

Hence the direction ratios of the given line are proportional to

So, the correct option is (a)

Straight Line in Space exercise Multiple choice question 6

Let point be and the point through which the line passes be (Given)

Also, the line is parallel to the vector

Now,

So, the correct option is

Straight Line in Space exercise Multiple choice question 7

So, the correct option is (c)

Straight Line in Space exercise Multiple choice question 8

using

And as the question states: A line makes angle with the axes respectively

So, the correct option is

Straight Line in Space exercise Multiple choice question 9

So let directional cosines be

Now, sum of the squares of directional cosines =1 (property)

So, direction cosines can be

So, the correct option is (A)

Straight Line in Space exercise Multiple choice question 10

Hence,

Now,

So, the correct option is

Straight Line in Space exercise Multiple choice question 11

that with .

Similarly

The line segment of the length and the direction cosines of the line segment are

Straight Line in Space exercise Multiple choice question 12

..........(1)

Direction ratios are 1,2,3

............(2)

Direction ratios are 1,2,3

Since, direction ratios of the two lines are equal so, the given lines are parallel.

So, the correct option is (a) parallel.

Straight Line in Space exercise Multiple choice question 13

Also the given line is parallel to the vector,

Let be perpendicular to the given line.

Now,

it is satisfied by the coordinates of z- axis, i.e, (0,0,1)

Hence, the given line is perpendicular to z – axis

So, the correct option is (d)

Straight Line in Space exercise Multiple choice question 14

Straight Line in Space exercise Multiple choice question 15

So, its distance from xy and yz plane is 0.

∴ By basic definition of 3-D coordinate we can say that x-coordinate and z-coordinate =0

∴ Any point on y-axis has x and z-coordinate =0

∴x=0 and z=0 Can be considered as the equation of y-axis.

Hence, the correct option is (A)

Straight Line in Space exercise Multiple choice question 16

Obviously parallel vectors b

So, the correct option is

Straight Line in Space exercise Multiple choice question 17

Any point on it

x-coordinate:

z-coordinate:

So, the correct option is (b) 4.

Straight Line in Space exercise Multiple choice question 18

∴ Parallel vectors b

And, hence the correct option is (D).

Chapter 27 of class 12 mathematics contains five exercises, ex 27.1 to ex 27.5. In addition to the sums given in these exercises, 18 multiple choice questions are given in the textbook. The concepts like finding the shortest distance between the lines, finding the x, y, z coordinates, projections of a line segment, direction ratios of perpendicular lines, equation of a plane and line passing through the given points, etc. The answers to these questions can be found easily using the RD Sharma Class 12 Chapter 27 MCQ guide. The students are advised to try the answers by themselves and recheck with the ones given in the solution guide.

It is essential to know the tricks and shortcuts to find the answers for the MCQs in an instant. The RD Sharma Class 12th Chapter 27 MCQ reference book contains all the possible methods in which these questions can be solved; students can use the ways they find easy to adapt. In addition, there are various practice questions to test the conceptual knowledge before tests and exams. All these questions are updated according to the latest NCERT syllabus. This makes the Class 12 RD Sharma Chapter 27 MCQ Solution book popular among CBSE school students.

The more MCQs are practiced, the more marks will be scored by the students. They can refer to the answers given in the RD Sharma Class 12 Solutions Straight Line in Space Chapter 27 MCQ book while doing homework or assignments. These solution books help the students in acquiring more marks in their public and JEE mains exams. Most of the students have a copy of the RD Sharma Class 12th Chapter 27 MCQ book to keep in touch with the practice.

The other big advantage is that the RD Sharma Class 12 Solutions Chapter 27 MCQ reference material can be downloaded for free from the Career 260 website. Visit this site now to obtain the copies of the RD Sharma books you require.

**RD Sharma Chapter-wise Solutions**

- Chapter 1 - Relations
- Chapter 2 - Functions
- Chapter 3 - Inverse Trigonometric Functions
- Chapter 4 - Algebra of Matrices
- Chapter 5 - Determinants
- Chapter 6 - Adjoint and Inverse of a Matrix
- Chapter 7 - Solution of Simultaneous Linear Equations
- Chapter 8 - Continuity
- Chapter 9 - Differentiability
- Chapter 10 - Differentiation
- Chapter 11 - Higher Order Derivatives
- Chapter 12 - Derivative as a Rate Measurer
- Chapter 13 - Differentials, Errors and Approximations
- Chapter 14 - Mean Value Theorems
- Chapter 15 - Tangents and Normals
- Chapter 16 - Increasing and Decreasing Functions
- Chapter 17 - Maxima and Minima
- Chapter 18 - Indefinite Integrals
- Chapter 19 - Definite Integrals
- Chapter 20 - Areas of Bounded Regions
- Chapter 21 - Differential Equations
- Chapter 22 - Algebra of Vectors
- Chapter 23 - Scalar Or Dot Product
- Chapter 24 - Vector or Cross Product
- Chapter 25 - Scalar Triple Product
- Chapter 26 - Direction Cosines and Direction Ratios
- Chapter 27 - Straight Line in Space
- Chapter 28 - The Plane
- Chapter 29 - Linear programming
- Chapter 30- Probability
- Chapter 31 - Mean and Variance of a Random Variable

1. Is the MCQ section challenging for the class 12 students?

The Multiple-choice questions section gives the equal advantage of gaining and losing marks in the examination. A good practice using the RD Sharma Class 12th Chapter 27 MCQ book will help the students face this section easily.

2. How can I obtain the RD Sharma books from an authorized site?

One of the top-rated educational websites, the Career 360 site, offers the authorized collection of the RD Sharma books for the welfare of the students, teachers, and other members who are in need of it.

3. How many MCQ questions are present in the 27th chapter of class 12 mathematics?

There are around 18 multiple choice questions given in the textbook in mathematics, chapter 27. The RD Sharma Class 12th Chapter 27 MCQ reference material will help in finding the right answers.

4. What is the minimum cost of each RD Sharma book available at the Career 360 website?

The entire collection of the RD Sharma books can be obtained from the Career 360 website without paying even a single penny. All these books are available for free here.

5. What are the advantages of using the RD Sharma solution books?

Answers are provided by experts.

Completely free to be accessed.

Updates according to the recent NCERT syllabus.

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