Exercise 10.2 of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra is based on the following topics:
- Addition of Vectors
- Properties of vector addition
- Multiplication of a Vector by a Scalar
- Components of a vector
- Vector joining two points
- Section formula
All these topics can be understood thoroughly by solving the problems given in this exercise. The solutions of all the problems of this exercise are given here.
Access Answers to NCERT Class 12 Maths Chapter 10- Vector Algebra Exercise 10.2 Page Number 440
Access Other Exercises of Class 12 Maths Chapter 10
Exercise 10.1 Solutions 5 Questions
Exercise 10.3 Solutions 18 Questions
Exercise 10.4 Solutions 12 Questions
Miscellaneous Exercise On Chapter 10 Solutions 19 Questions
Access Answers to NCERT Class 12 Maths Chapter 10 Exercise 10.2
1. Compute the magnitude of the following vectors:
Given vectors are:
2. Write two different vectors having same magnitude.
3. Write two different vectors having same direction.
Two different vectors having same directions are:
4. Find the values of x and y so that the vectors are equal
will be equal only if their corresponding components are equal.
Thus, the required values of x and y are 2 and 3 respectively.
5. Find the scalar and vector components of the vector with initial point (2, 1) and terminal point (–5, 7).
The scalar and vector components are:
The vector with initial point P (2, 1) and terminal point Q (–5, 7) can be shown as,
Thus, the required scalar components are –7 and 6 while the vector components are
6. Find the sum of the vectors
Let us find the sum of the vectors:
7. Find the unit vector in the direction of the vector
We know that
8. Find the unit vector in the direction of vector , where P and Q are the points
(1, 2, 3) and (4, 5, 6), respectively
We know that,
9. For given vectors, and , find the unit vector in the direction of the vector
We know that,
10. Find a vector in the direction of vector which has magnitude 8 units.
11. Show that the vectorsare collinear.
Therefore, we can say that the given vectors are collinear.
12. Find the direction cosines of the vector
13. Find the direction cosines of the vector joining the points A (1, 2, –3) and
B (–1, –2, 1) directed from A to B.
We know that the
Given points are A (1, 2, –3) and B (–1, –2, 1).
14. Show that the vector is equally inclined to the axes OX, OY, and OZ.
15. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are respectively, in the ratio 2:1
We know that
The position vector of point R dividing the line segment joining two points
P and Q in the ratio m: n is given by:
16. Find the position vector of the mid point of the vector joining the points P (2, 3, 4) and Q (4, 1, – 2).
The position vector of mid-point R of the vector joining points P (2, 3, 4) and Q (4, 1, – 2) is given by,
17. Show that the points A, B and C with position vectors,, respectively form the vertices of a right angled triangle.
Given position vectors of points A, B, and C are:
Hence, proved that the given points form the vertices of a right angled triangle.
18. In triangle ABC (Fig 10.18) which of the following is not true:
Firstly let us consider,
19. If are two collinear vectors, then which of the following are incorrect:
A. , for some scalar λ
C. the respective components of are proportional
D. both the vectors have same direction, but different magnitudes