If either then Is the converse true? Justify your answer with an example.

Mathematics Part-II

Book: Mathematics Part-II

Chapter: 10. Vector Algebra

Subject: Maths - Class 12^th

Q. No. 8 of Exercise 10.4

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8

If either then Is the converse true? Justify your answer with an example.

(where θ is the angle between the vectors)

If

Similarly, If

Now, If

(where θ is the angle between the vectors)

This implies that the converse is not always true. The vectors may not be zero but the angle between is 90°, i.e. the vectors are perpendicular.

8

Chapter Exercises

Exercise 10.1

Exercise 10.2

Exercise 10.3

Exercise 10.4

Miscellaneous Exercise

1

Find if

2

Find a unit vector perpendicular to each of the vector

3

If a unit vector makes angles and an acute angle θ with then find θ and hence, the components of .

4

Show that

5

Find λ and μ if

6

Given that What can you conclude about the vectors ?

7

Let the vectors be given as Then show that

8

If either then Is the converse true? Justify your answer with an example.

9

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

10

Find the area of the parallelogram whose adjacent sides are determined by the vectors

11

Let the vectors be such that then is a unit vector, if the angle between is

12

Area of a rectangle having vertices A, B, C and D with position vectors respectively is