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Planning a schedule that every 12th grader must follow to keep in touch with their ongoing syllabus and preparing for the board exams is essential. This task can be accomplished easily only with the help of the right reference books. Many students struggle with mathematics to arrive at the right solution in various concepts. If any student faces challenges in the Straight Line in Space topic, they can refer to the RD Sharma Class 12th Chapter 27 VSA book.

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Straight Line in Space Exercise Very Short Answer Question 1

Required answer is

Use properties of vector

Cartesian and vector equation of x-axis

Since x-axis passes through the point having position vector

and parallel to the vector having direction ratios proportional to 1, 0, 0.

The Cartesian equation of x-axis is

Also its vector equation is

Straight Line in Space Exercise Very Short Answer Question 2

Required answer is

Use properties of vector

Cartesian and vector equation of y-axis

Since y-axis passes through the point having position vector

and is parallel to the vector having direction ratios proportional to 0, 1, 0

The Cartesian equation of y-axis is

Also the vector equation is

Straight Line in Space Exercise Very Short Answer Question 3

Required answer is

Use properties of vector

Cartesian and vector equation of z-axis

Since z-axis passes through the point having position vector

and is parallel to the vector having direction ratios proportional to 0, 0, 1

The Cartesian of z-axis is

Also its vector equation

Striaght Line in Space Exercise Very Short Answer question 4

Required answer is

Use properties of vector

Vector is parallel to vector

The vector equation of the line passing through the point having position vector and parallel to the vector is

Straight Line in Space Exercise Very Short Answer question 5

Required answer is

Use properties of vector

We have

Now the equation of the line AB can be rewritten as,

The direction ratios of the line parallel to AB proportional to

Straight Line in Space Exercise Very Short Answer question 6

Required answer is

Use properties of vector

We have

The equation of the given line can be rewritten as,

The direction ratios of the line parallel to AB are proportional to

The direction cosines of the line parallel to AB are proportional to

Straight Line in Space Exercise Very Short Answer Question 7

Required answer is

Use properties of vector

We have,

The equation of the given line can be rewritten as,

The direction ratios of the line parallel to AB are proportional to 4, -3, 1

The direction cosines of the line parallel to AB proportional to

Straight Line in Space Exercise Very Short Answer Question 8

The given line is perpendicular to z-axis

Use properties of vector

We have

The given line is parallel to the vector

Let, be perpendicular to the given line

Now,

Direction ratios are

Check perpendicular condition with x axis

Direction ratio of x axis is

Hence x axis is not perpendicular

Check perpendicular condition with y axis

Direction ratio of y axis is

Hence y axis is not perpendicular

Check perpendicular condition with z axis

Direction ratio of z axis is

Hence, the given line is perpendicular to the z-axis

Straight Line in Space Exercise Very Short Answer Question 9

Required answer is

Use properties of vector

We have,

The given lines are parallel to the vectors

Let be the angle between the given lines

Now,

Straight Line of Space Excercise Very Short Anwer Question 10

Required answer is

Use equation of a line in space.

Cartesian equations are

We have,

The equation of the given line can be rewritten as,

The direction ratios of the line parallel to AB are proportional to

The direction cosines of the line parallel to AB are proportional to

Straight Line of Space Excercise Very Short Anwer Question 11

Required answer is

Use formula

We have,

The given lines can be rewritten as,

These lines are parallel to vectors

Let be the angle between these lines.

Now,

Straight Line of Space Excercise Very Short Anwer Question 12

Required answer is

Use equation of line in space

We have,

The given lines are parallel to vectors

Now, for we must have,

Straight Line in Space Exercise Very Short Answer Question 13

Required answer is

Use equation of line in space

The shortest distance between the parallel lines

is given by,

Straight Line in Space Exercise Very Short Answer Question 14

Required answer is

Use formula

The shortest distance between the lines is given by

For the lines to be intersecting,

Straight Line in Space Exercise Very Short Answer Question 15

Required answer is

Use equation of line in space

We have,

The equation of the given line can be rewritten as,

The direction ratios of the line parallel to AB are proportional to

The direction cosines of the line parallel to AB are proportional to,

Straight Line in Space Exercise Very Short Answer question 16

Required answer is

Use equation of line in space

We have,

The equation of the line AB can be rewritten as,

Thus, the direction ratios of the line parallel to AB are proportional to

Straight Line in Space Exercise Very Short Answer question 17

Required answer is

Use properties of vector

We have,

The given line passes through the point and has direction ratios proportional to

Vector equation of the given line passing through the point having position vector

and parallel to a vector is

Straight Line in Space Exercise Very Short Answer question 18

Required answer is

Use the equation of a line in space.

We have,

The equation of the given line can be rewritten as,

The direction ratios of the line parallel to the given line are proportional to

The direction cosines of the line parallel to the given line are proportional to

Straight Line in Space Exercise Very Short Answer question 19

Required answer is

Use the equation of a line in space.

Point

Line

The equation of the given line is

Since the required line is parallel to the given line, the direction ratios of the required line are proportional to

Hence the Cartesian equation of the line passing through the point and parallel to a vector having direction ratios proportional to is

Straight Line in Space Exercise Very Short Answer Question 20

Required answer is

Use the equation of a line in space.

Let be the angle between the given lines

The given lines are parallel to the vectors respectively

So, the angle between the given lines are given by

Straight Line in Space Exercise Very Short Answer Question 21

Required angle is

Use equation of a line in space.

The equation of the given lines can be rewritten as,

We know that angle between the lines

is given by,

Let,

Let be the angle between the given lines

Thus, the angle between the given lines is

Straight Line in Space Exercise Very Short Answer Question 22

**Answer:**

Required answer is **Hint:**

Use equation of a line in space.**Given:**

Point and parallel vector **Solution:**

The line is passing through the point through the point having position vector is and parallel to the vector

Also, see,

RD Sharma Solutions Class 12 mathematics chapter 27 exercise 27.1

RD Sharma Solutions Class 12 mathematics chapter 27 exercise 27.2

RD Sharma Solutions Class 12 mathematics chapter 27 exercise 27.3

RD Sharma Solutions Class 12 mathematics chapter 27 exercise 27.4

RD Sharma Solutions Class 12 mathematics chapter 27 exercise 27.5

RD Sharma Solutions Class 12 mathematics chapter 27 exercise MCQ

RD Sharma Solutions Class 12 mathematics chapter 27 exercise FBQ

The number of exercises in class 12, chapter 27, Straight Line in Space, is five. The concepts in the ex 27.1 to ex 27.5 are included in the Very Short Answers part, where there are 22 questions in total. The topics from which the questions are asked include finding the angle between the lines, symmetric and unsymmetric, vector equations, cartesian equations, equation of a plane, equation of a line, direction cosines, conditions for lines to intersect, direction cosine, etc. The RD Sharma Class 12 Chapter 27 VSA solution guide directs the students on how these sums can be solved easily.

Students cannot contact their teachers or tutors every time a doubt strikes them; simple and complex doubts will also vanish when a glance is made into the RD Sharma Class 12th Chapter 27 VSA reference book. The various practice questions in this book will motivate the students to work out more sums that eventually sharpen their knowledge. Soon, they would cross their benchmark scores effortlessly due to the high confidence level they gained from the practice.

The Class 12 RD Sharma Chapter 27 VSA Solution book is updated according to the recent NCERT pattern. And it also provides additional benefits for the students who refer to these books. The well-known source from where most of the teachers pick questions to conduct tests is the RD Sharma books. Therefore, when a student uses the RD Sharma Class 12 Solutions Straight Line in Space Chapter 27 VSA, he is getting ready for his tests and exams.

As the Career 360 website provides all the RD Sharma solution books, including the RD Sharma Class 12th Chapter 27 VSA, for free of cost, many students flock to this website to get a copy. In addition, due to the presence of the Download option, it is easier to save the PDF material at your device to access it offline. As a result, a great number of students have benefitted from using these books. So, download your copy of RD Sharma Class 12 Solutions Chapter 27 VSA and start your preparation for the board exams.

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 23: 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 23: Scalar and dot products

Chapter 17: Maxima and Minima

Chapter 123: 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 223: The plane

Chapter 29: Linear programming

Chapter 30: Probability

Chapter 31: Mean and variance of a random variable

1. Which is the top-rated solution book for the students to refer to the Chapter 27 VSA?

The RD Sharma Class 12th Chapter 27 VSA is the top-rated reference material with positive feedback from the students and the teachers.

2. Can the RD Sharma book be bought from the nearby stores?

You need not search for the RD Sharma books in stores when present on the Career 360 website for free of cost.

3. How much do the RD Sharma books cost to be accessed online?

To access and view the RD Sharma books online at the Career 360 website, you need not pay any money as it is available for free of cost.

4. What makes the RD Sharma solution books the best to refer to the VSA section?

The sums in the VSA section must be solved instantly using various tricks and formulas. The RD Sharma Class 12th Chapter 27 VSA book consists of all suck tricks and techniques to solve these sums effortlessly.

5. Are the RD Sharma books based on the NCERT pattern?

Yes, the RD Sharma reference guides are based on the latest NCERT syllabus.

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