NCERT Solution Class 12 Chapter 10- Vector Algebra Miscellaneous Exercise

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise – CBSE Term II Free PDF Download

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 include:

  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 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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ncert sol Class 12 maths chapter 10 ex mis 11

Access Other Exercises of Class 12 Maths Chapter 10 Vector Algebra

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 to NCERT Class 12 Maths Chapter 10 Vector Algebra Miscellaneous Exercise

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

Solution:

Let us consider,

NCERT Solutions Class 12 Mathematics Chapter 10- image 133

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

Solution:

Firstly let us consider,

NCERT Solutions Class 12 Mathematics Chapter 10- image 134

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:

It is given that,

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 12 Mathematics Chapter 10- image 135

NCERT Solutions Class 12 Mathematics Chapter 10- image 136

NCERT Solutions Class 12 Mathematics Chapter 10- image 1404. IfNCERT Solutions Class 12 Mathematics Chapter 10- image 137, then is it true thatNCERT Solutions Class 12 Mathematics Chapter 10- image 138? Justify your answer.

Solution:

It is given that,

NCERT Solutions Class 12 Mathematics Chapter 10- image 139

NCERT Solutions Class 12 Mathematics Chapter 10- image 141

5. Find the value of x for whichNCERT Solutions Class 12 Mathematics Chapter 10- image 142is a unit vector.

Solution:

We know,

NCERT Solutions Class 12 Mathematics Chapter 10- image 143

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

NCERT Solutions Class 12 Mathematics Chapter 10- image 144.

Solution:

Let us consider the,

NCERT Solutions Class 12 Mathematics Chapter 10- image 145

7. IfNCERT Solutions Class 12 Mathematics Chapter 10- image 146, find a unit vector parallel to the vectorNCERT Solutions Class 12 Mathematics Chapter 10- image 147.

Solution:

Let us consider the given vectors,

NCERT Solutions Class 12 Mathematics Chapter 10- image 148

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:

Firstly let us consider,

NCERT Solutions Class 12 Mathematics Chapter 10- image 149

NCERT Solutions Class 12 Mathematics Chapter 10- image 150

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 12 Mathematics Chapter 10- image 151externally in the ratio 1: 2. Also, show that P is the midpoint of the line segment RQ.

Solution:

We know,

NCERT Solutions Class 12 Mathematics Chapter 10- image 152

10. The two adjacent sides of a parallelogram areNCERT Solutions Class 12 Mathematics Chapter 10- image 153and NCERT Solutions Class 12 Mathematics Chapter 10- image 154.

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

Solution:

Firstly let us consider,

NCERT Solutions Class 12 Mathematics Chapter 10- image 155

NCERT Solutions Class 12 Mathematics Chapter 10- image 156

11. Show that the direction cosines of a vector equally inclined to the axes OX, OY and OZ areNCERT Solutions Class 12 Mathematics Chapter 10- image 157.

Solution:

Firstly,

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 12 Mathematics Chapter 10- image 158

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

NCERT Solutions Class 12 Mathematics Chapter 10- image 159

Hence proved.

NCERT Solutions Class 12 Mathematics Chapter 10- image 160

Solution:

Assume,

NCERT Solutions Class 12 Mathematics Chapter 10- image 161

NCERT Solutions Class 12 Mathematics Chapter 10- image 162

13. The scalar product of the vectorNCERT Solutions Class 12 Mathematics Chapter 10- image 163with a unit vector along the sum of vectors NCERT Solutions Class 12 Mathematics Chapter 10- image 164and NCERT Solutions Class 12 Mathematics Chapter 10- image 165is equal to one. Find the value ofNCERT Solutions Class 12 Mathematics Chapter 10- image 166.

Solution:

Let’s consider the

NCERT Solutions Class 12 Mathematics Chapter 10- image 167

14. If NCERT Solutions Class 12 Mathematics Chapter 10- image 168are mutually perpendicular vectors of equal magnitudes, show that the vector NCERT Solutions Class 12 Mathematics Chapter 10- image 169is equally inclined to NCERT Solutions Class 12 Mathematics Chapter 10- image 170andNCERT Solutions Class 12 Mathematics Chapter 10- image 171.

Solution:

Lets assume,

NCERT Solutions Class 12 Mathematics Chapter 10- image 172

Hence proved.

15. Prove thatNCERT Solutions Class 12 Mathematics Chapter 10- image 173, if and only if NCERT Solutions Class 12 Mathematics Chapter 10- image 174are perpendicular, givenNCERT Solutions Class 12 Mathematics Chapter 10- image 175.

Solution:

It is given that

NCERT Solutions Class 12 Mathematics Chapter 10- image 176

Hence proved.

NCERT Solutions Class 12 Mathematics Chapter 10- image 177

Solution:

Explanation:

NCERT Solutions Class 12 Mathematics Chapter 10- image 178

NCERT Solutions Class 12 Mathematics Chapter 10- image 179

NCERT Solutions Class 12 Mathematics Chapter 10- image 180

Solution:

Explanation:

NCERT Solutions Class 12 Mathematics Chapter 10- image 181

Hence the correct answer is D.

18. The value of NCERT Solutions Class 12 Mathematics Chapter 10- image 182is

(A) 0 (B) –1 (C) 1 (D) 3

Solution:

Explanation:

It is given that,

NCERT Solutions Class 12 Mathematics Chapter 10- image 183

Hence the correct answer is C.

NCERT Solutions Class 12 Mathematics Chapter 10- image 184

Solution:

Explanation:

NCERT Solutions Class 12 Mathematics Chapter 10- image 185

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