NCERT Solution Class 12 Chapter 10- Vector Algebra Miscellaneous Exercise

The Miscellaneous Exercise of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra is based on all the topics covered in this chapter. The main topics that are covered in this chapter includes:

  1. Basic Concepts of Vector Algebra
  2. Types of Vectors
  3. Addition of Vectors
  4. Multiplication of a Vector by a Scalar
  5. Product of Two Vectors

Miscellaneous exercise provides questions from all the topics provided in the chapter. Solving these questions helps the students in a quick revision of the chapter.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra Miscellaneous Exercise

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Access other exercises of Class 12 Maths Chapter 10

Exercise 10.1 Solutions 5 Questions

Exercise 10.2 Solutions 19 Questions

Exercise 10.3 Solutions 18 Questions

Exercise 10.4 Solutions 12 Questions

Access Answers of Maths NCERT Class 12 Chapter 10 Miscellaneous

1. Write down a unit vector in XY-plane, making an angle of 30° with the positive direction of x-axis.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 1

2. Find the scalar components and magnitude of the vector joining the points P (x1, y1, z1) and Q (x2, y2, z2).

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 2

3. A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

Solution:

Let O and B be the initial and final positions of the girl respectively.

Then, the girl’s position can be shown as:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 3

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 4

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 94. IfNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 5, then is it true thatNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 6? Justify your answer.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 7

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 8

5. Find the value of x for whichNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 10is a unit vector.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 11

6. Find a vector of magnitude 5 units, and parallel to the resultant of the vectors

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 12.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 13

7. IfNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 14, find a unit vector parallel to the vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 15.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 16

8. Show that the points A (1, –2, –8), B (5, 0, –2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 17

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 18

9. Find the position vector of a point R which divides the line joining two points P and Q whose position vectors areNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 19externally in the ratio 1: 2. Also, show that P is the mid point of the line segment RQ.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 20

10. The two adjacent sides of a parallelogram areNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 21and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 22.

Find the unit vector parallel to its diagonal. Also, find its area.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 23

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 24

11. Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ areNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 25.

Solution:

Let’s assume a vector to be equally inclined to axes OX, OY, and OZ at angle α.

Then, the direction cosines of the vector are cos α, cos α, and cos α.

Now, we know that

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 26

Therefore, the direction cosines of the vector which are equally inclined to the axes are

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 27.

12. Let NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 28andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 29. Find a vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 30which is perpendicular to both NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 31andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 32, andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 33.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 34

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 35

13. The scalar product of the vectorNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 36with a unit vector along the sum of vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 37and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 38is equal to one. Find the value of λ.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 39

14. If NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 40are mutually perpendicular vectors of equal magnitudes, show that the vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 41is equally inclined to NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 42andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 43.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 44

15. Prove thatNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 45, if and only if NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 46are perpendicular, givenNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 47.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 48

16. If θ is the angle between two vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 49and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 50, then NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 51only when

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 52

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 55

17. Let NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 56 and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 57 be two unit vectors andθ is the angle between them. Then NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 58is a unit vector if

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 59

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 60

18. The value of NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 61is

(A) 0 (B) –1 (C) 1 (D) 3

Solution:

Given,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 62

The correct answer is C.

19. If θ is the angle between any two vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 63andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 64, then NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 65when θ is equal to

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 66

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra miscellaneous ex- 67

1 Comment

  1. excellent work

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