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RS Aggarwal - Mathematics

27. Straight Line in Space

1. Relation
2. Functions
3. Binary Operations
4. Inverse Trigonometric Functions
5. Matrices
6. Determinants
7. Adjoint and Inverse of a Matrix
8. System of Linear Equations
9. Continuity and Differentiability
10. Differentiation
11. Applications of Derivatives
12. Indefinite Integral
13. Method of Integration
14. Some Special Integrals
15. Integration Using Partial Fractions
16. Definite Integrals
17. Area of Bounded Regions
18. Differential Equations and Their Formation
19. Differential Equations with Variable Separable
20. Homogeneous Differential Equations
21. Linear Differential Equations
22. Vectors and Their Properties
23. Scalar, or Dot, Product of Vectors
24. Cross, or Vector, Product of Vectors
25. Product of Three Vectors
26. Fundamental Concepts of 3-Dimensional Geometry
27. Straight Line in Space
28. The Plane
29. Probability
30. Bayes’s Theorem and its Applications
31. Probability Distribution
32. Binomial Distribution
33. Linear Programming

Exercise 27A

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Exercise 27B

Exercise 27C

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Exercise 27D

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Exercise 27E

Exercise 27F

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Objective Questions

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19

Q. 20

Find the vector equation of a line passing through the point A(3, -2, 1) and parallel to the line joining the points B(-2, 4, 2) and C(2, 3, 3). Also, find the Cartesian equations of the line.

Class 12th RS Aggarwal - Mathematics 27. Straight Line in Space

Answer :

Given: line passes through the point (3, -2, 1) and is parallel to the line joining points B(-2, 4, 2) and C(2, 3, 3).

To find: equation of line in vector and Cartesian forms

Formula Used: Equation of a line is

Vector form:

Cartesian form:

where is a point on the line and with b₁ : b₂ : b₃ being the direction ratios of the line.

Explanation:

Here,

The direction ratios of the line are (-2 - 2) : (4 - 3) : (2 - 3)

⇒ -4 : 1 : -1

⇒ 4 : -1 : 1

So,

Therefore,

Vector form:

Cartesian form:

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PREVIOUSFind the vector and Cartesian equations of the line joining the points whose position vectors are and NEXTFind the vector equation of a line passing through the point having the position vector and parallel to the line joining the points with position vectors and Also, find the Cartesian equivalents of this equation.

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