NCERT Solution Class 12 Chapter 10- Vector Algebra Exercise 10.4

The Exercise 10.4 of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra is based on vector (or cross) product of two vectors. The concept of distributivity of vector product over addition is also explained before this exercise. The magnitude of the vector product of two vectors can be constructed by taking the product of the magnitudes of the vectors times the sine of the angle (<180 degrees) between them. There are problems present in this exercise which are based on this definition of vector products as well.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 10- Vector Algebra Exercise 10.4

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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

Miscellaneous Exercise On Chapter 10 Solutions 19 Questions

Access Answers of Maths NCERT Class 12 Chapter 10.4

1. FindNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 1, if NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 2andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 3

Solution:

We have,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 4

2. Find a unit vector perpendicular to each of the vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 5andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 6, where NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 7andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 8.

Solution:

We have,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 9

3. If a unit vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 10 makes an anglesNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 11with NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 12with NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 13and an acute angle θ withNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 14, then find θ and hence, the compounds ofNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra - 1.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 15

4. Show that

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 16

Solution:

Taking the LHS, we have

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 17

5. Find λ and μ if NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 18.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 19

6. Given that NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 20 andif. What can you conclude about the vectorsNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 22?

Solution:

Given,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 23

7. Let the vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 24given asNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 25 NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 26. Then show that NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 27

Solution:

We have,

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 28

8. If either NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 29 orNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 30, thenNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 31. Is the converse true? Justify your answer with an example.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 32

9. Find the area of the triangle with vertices A (1, 1, 2), B (2, 3, 5) and C (1, 5, 5).

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 33

10. Find the area of the parallelogram whose adjacent sides are determined by the vector NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 34.

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 35

11. Let the vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 36and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 37be such that NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 38andNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 39, thenNCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 40 is a unit vector, if the angle between NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 41and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 42is

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 43

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 44

12. Area of a rectangle having vertices A, B, C, and D with position vectors NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 45and NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 46 respectively is

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 47

Solution:

NCERT Solutions Class 11 Mathematics Chapter 10 Vector Algebra ex.10.4 - 48

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