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The RD Sharma class 12 solution of Straight line in space exercise 27.3 is used by thousands of students and teachers for the practical knowledge of maths. The RD Sharma class 12th exercise 27.3 consists of 10 questions including subparts which explores vector and cartesian form, finding the point of intersection between the two lines.

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Straight Line in Space exercise 27.3 question 1

and …(ii)

Then

Substituting in eqn (ii)

Taking first and second ratios, we get

Now taking second and third ratios, we get

The line intersects at a point

taking

Points will be

Straight Line in Space exercise 27.3 question 2

The co-ordinates of first line is

The co- ordinates of any point on the second line are given by

The co-ordinates of second line is

If the line intersect, then they have a common point. So, for some value of λ and μ.

We must have,

Solving (i)and (ii), we get

Substituting in (iii)

This shows that the given line will not intersect each other.

Straight Line in Space exercise 27.3 question 3

So, the co-ordinates of a general point on this line are

The equation of second line is given

So, the co-ordinates of general point on this line are

If the line intersect, then they have a common point. So, for some value of λ and μ,we must have

Solving the first two equations (i) and (ii), we get

Since, satisfying the eqn(iii)

Hence,the given lines intersect each other.

When

the co-ordinates of the required point of intersection are

Straight Line in Space exercise 27.3 question 4

The co-ordinates of general point on are

The co-ordinates of any point on the line are given by

The co-ordinates of general point on are

If the line intersect, then they have a common point. So, for some value of λ and μ.

We must have,

Solving (ii) and (iii), we get

Substituting in (i),we get

Since satisfying eqn(iii),

Hence, the given line intersect.

Substituting the value of λ and μ in the Co- ordinates of a general point on the line and , we get

Hence, and intersect at point

Straight Line in Space exercise 27.3 question 5

Lines intersect if

From (ii) and (iii),

Substituting in equation (i)

Since, is true.

Hence, the lines intersect.

Point of intersection is :

Straight Line in Space exercise 27.3 question 6(i)

Then,

Equations we get,

Solving equation (ii) and (iii), we get

Which doesn’t satisfy the equation (i) which is a contradiction.

Thus, the above lines are skew lines i.e. they neither intersect nor parallel to each other.

Straight Line in Space exercise 27.3 question 6(ii)

The first line passes through the point (1,-1,0) and has direction ratio proportional to 2,3,1 and its vector equation is

…(i)

Here,

Also, the second line passes through the point and has direction ratios proportional to

Its vector equation is

...........(ii)

Here,

Now,

And

We observe ,

Thus,the given lines don't intersect.

Straight Line in Space exercise 27.3 question 6(iii)

Co-ordinate of second equation of line

If the lines intersect, then they have a common point for some value of λ and μ.

Satisfy equation (iii). So, the given line intersect and the point of intersection is

Straight Line in Space exercise 27.3 question 6(iv)

So, the co-ordinates of a general point on this line are

The equation of the second line,

So, the co-ordinates of a general point on this line are (

If the lines intersect, then they have a common point for some value of λ and μ

We have,

Putting the value of μ from equation (ii) to (i), we get

Now putting the value of λ in equation (ii), we get

As we can see by putting the value of λ and μ in equation (iii), that it satisfy the equation

Check,

Hence intersection point exists or line of intersects.

Thus, point of intersection

Straight Line in Space exercise 27.3 question 7

Co-ordinate of any random point on are and on are

If the lines Mand N intersect then ,they must have a common point on them i.e. P and Q must coincide for some values of λ and μ.

Now,

Solving (i) and (ii) ,we get

Substitute the value in equation (iii),

So, the given line intersect each other.

Now, point of intersection is

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RD Sharma class 12 solutions chapter 27 exercise 27.3 material is prepared by a group of subject experts who have immense knowledge about CBSE question paper patterns. Each answer goes through a series of quality checks to ensure that the best information is available.

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**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. Who is this material for?

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3. How are RD Sharma books better than NCERT?

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