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

The class 12 students work hard on preparing for their public exams. They do not get much time in visiting tuitions for extra classes beyond the school timings. A subject like mathematics requires many tricks to solve the sums quickly during examinations. The Straight Line in Space is a challenging concept that is tricky for the students to solve. RD Sharma solutions Best solution guides like the RD Sharma Class 12th Chapter 27 FBQ lend a helping hand to the class 12 students to understand the concept in-depth.

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Straight Line in Space Exercise Fill in the blanks Question 1

Straight Line in Space Exercise Fill in the blanks Question 2

By comparing with equation

The given line passes through the point (x1 , x2, x3)

i.e. (5 , -4 , 6) and direction ratios are (a ,b ,c) i.e. (-3 , 7 ,2)

Now , we can write vector equation of the line as

Straight Line in Space Exercise Fill in the blanks Question 3

∴ vector equation

Straight Line in Space Exercise Fill in the blanks question 4

We know that ,

Straight Line in Space Exercise Fill in the blanks question 5

By using direction ratios of line

Straight Line in Space Exercise Fill in the blanks question 6

OX , OY and OZ are -----------

And having direction cosines l,m,n is

Also line is equally inclined to co-ordinate axes

Here

∴ Equation of line is

Straight Line in Space Exercise Fill in the blanks Question 7

Let θ be angle between given lines

Straight Line in Space Exercise Fill in the blanks Question 8

Equation of line passing through and having drs ;l,m,n is

Hence

So, Equation of line

Straight Line in Space Exercise Fill in the blanks Question 9

Since, the line passes through ( a, b , c)

Thus , its equation is

Straight Line of Space Excercise Fill in the blanks Question 10

as the lines are at right angle

Straight Line of Space Excercise Fill in the blanks Question 11

a = 2 , b =1 , c = -1

another line passing through P ( 1 , 1 , 2)

we can assume it as position vector and parallel to given line so normal vector will be same .

Eq. of line is given by

Here

Straight Line of Space Excercise Fill in the blanks Question 12

Point ( x , 0 , 0) points on z axis.

Straight Line in Space Exercise Fill in the blanks Question 13

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

∴ By basic definition of 3-D coordinate we can say that

x-coordinate and z-coordinate are 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 answer is

Straight Line in Space Exercise Fill in the blanks Question 14

-----1

-------3

Now [Using scalar triple formula]

Substituting the values in Numerator

Straight Line in Space Exercise Fill in the blanks Question 15

-------1

------2

[ If a,b,c are coplanar ]

So , the value of

Straight Line in Space Exercise Fill in the blanks question 16

of a line does not make it possible to find the slope of a line

∴ x in symmetric form

Straight Line in Space Exercise Fill in the blanks question 17

Point ( x, 0, 0 ) points on x-axis.

Straight Line in Space Exercise Fill in the blanks question 18

And position vector of ( 1 , -1 , 6) is

Also,

The vector equation of a line which passes through two

Points whose position vectors are is

Hence , required equation of line is

Straight Line in Space Exercise Fill in the blanks Question 19

By comparing with equation

We get given line passes through the point (x1 , x2, x3)

i.e. (5 , -4 , 6) and direction ratios are (a ,b ,c) i.e. ( 3 , 7 , 2)

Now , we can write vector equation of the line as

Straight Line in Space Exercise Fill in the blanks Question 20

**Answer :** Perpendicular**Hint :** Angle should be **Given :** The line of shortest distance between two skew-lines is

-------- to both the lines.**Solution :** The line of shortest distance between two skew-lines is

perpendicular to both the lines.

Two or more lines which have no intersections but are not parallel are called skew lines

Class 12, mathematics, chapter 27, Straight Line in Space consists of 5 exercises, ex 27.1 to ex 27.5. There are 20 questions in the Chapter 27 FBQ section. The concepts present in this section are vector equations, cartesian equations, direction ratios, the shortest distance between the lines, direction cosines, equation of a plane, angle between two lines, etc. Even though the chapter is a little easy, when the students are asked these questions in the Fill in the Blanks format, they tend to get confused. And this is why the role of the RD Sharma class 12 Chapter 27 FBQ solution book is inevitable.

All the answers provided in the RD Sharma Class 12th Chapter 27 FBQ book are framed by a team of mathematical experts. They have contributed their knowledge and skill for the welfare of the students. However, only with a good amount of practice, this section can be attended with full confidence. Here is where the additional practice questions present in the Class 12 RD Sharma Chapter 27 FBQ Solution play a major role. The more sums students work out, the better they understand the concept and increase the speed in completing the sums.

A top-rated educational website, Career 360 provides the RD Sharma Class 12 Solutions Straight Line in Space Chapter 27 FBQ and the other RD Sharma reference books for free of cost. No one is required to pay even a minimum amount of monetary charge to own the complete set of these books. Most of the teachers frame their questions papers from the questions picked from the RD Sharma Class 12th Chapter 27 FBQ reference book. Therefore, practicing with this set of books beforehand makes the students familiar with the sums during the tests and exams.

Every student who has used the RD Sharma Class 12 Solutions Chapter 27 FBQ has opened up their opinions that they have benefitted a lot from using it. So now, it is your time to own a copy of the RD Sharma books to prepare for your tests and 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 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. What is the most suggested solution guide for the class 12 students to refer to the chapter 27 FBQ section?

The RD Sharma Class 12th Chapter 27 FBQ is the most suggested solution book for the students to refer to the Fill in the blanks section.

2. Where can I find the RD Sharma books at a minimum cost?

The RD Sharma books can be found for free of cost at the Career 360 website. In addition, you can find the entire RD Sharma books collection here.

3. Are FBQs tough to answer?

The FBQ section is always a bit tricker. But with the constant practice using the RD Sharma Class 12th Chapter 27 FBQ solution guide, you can face such questions easily in the examination.

4. Does the RD Sharma book provide answers for every question given in the textbook?

The RD Sharma books provide answers for all the questions present in the textbook and additional practice questions.

5. Is it easy to acquire the PDF format of the RD Sharma solution books?

The PDF format of the RD Sharma solution books can be obtained easily by clicking the Download button on the Career 360 website.

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