RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 24. Cross, or Vector, Product of Vectors

Subject: Maths - Class 12th

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Exercise 24

1 A

Find and , when

and


1 B

Find and , when

and


1 C

Find and , when

and


1 D

Find and , when

and


1 E

Find and , when

and


2

Find λ if .
3

If and , find .

Verify that (i) and are perpendicular to each other


and (ii) and are perpendicular to each other.
4

Find the value of:

i. ii. iii.


5 A

Find the unit vectors perpendicular to both and when

and


5 B

Find the unit vectors perpendicular to both and when

and


5 C

Find the unit vectors perpendicular to both and when

and


5 D

Find the unit vectors perpendicular to both and when

and


6

Find the unit vectors perpendicular to the plane of the vectors

and


7

Find a vector of magnitude 6 which is perpendicular to both the vectors

and .
8

Find a vector of magnitude 5 units, perpendicular to each of the vectors

and, where and


9

Find an angle between two vectors and with magnitudes 1 and 2 respectively and .
10

If , and , find a vector which is perpendicular to both and and for which .
11

If , and , find a vector which is perpendicular to both and and for which .
12

Prove that , where θ is the angle between and .
13

Write the value of p for which and are parallel vectors.
14 A

Verify that , when

, and


14 B

Verify that , when

, and .
15 A

Find the area of the parallelogram whose adjacent sides are represented by the vectors:

and


15 B

Find the area of the parallelogram whose adjacent sides are represented by the vectors:

and


15 C

Find the area of the parallelogram whose adjacent sides are represented by the vectors:

and


15 D

Find the area of the parallelogram whose adjacent sides are represented by the vectors:

and


16 A

Find the area of the parallelogram whose diagonal are represented by the vectors

and


16 B

Find the area of the parallelogram whose diagonal are represented by the vectors

and


16 C

Find the area of the parallelogram whose diagonal are represented by the vectors

and .
17 A

Find the area of the triangle whose two adjacent sides are determined by the vectors

and


17 B

Find the area of the triangle whose two adjacent sides are determined by the vectors

and .
18 A

Using vectors, find the area of ΔABC whose vertices are

A(1, 1, 2), B(2, 3, 5) and C(1, 5, 5)
18 B

Using vectors, find the area of ΔABC whose vertices are

A(1, 2, 3), B(2, −1, 4) and C(4, 5, Δ1) ((considering Δ1 as 1 ))
18

Using vectors, find the area of ΔABC whose vertices are

A(3, −1, 2), B(1, −1, −3) and C(4, −3, 1)
18 D

Using vectors, find the area of ΔABC whose vertices are

A(1, −1, 2), B(2, 1, −1) and C(3, −1, 2).
19

Using vector method, show that the given points A, B, C are collinear:

A(3, −5, 1), B(−1, 0, 8) and C(7, −10, −6)
19 B

Using vector method, show that the given points A, B, C are collinear:

A(6, −7, −1), B(2, −3, 1) and C(4, −5, 0).
20

Show that the point A, B, C with position vectors , and respectively are collinear.
21

Show that the points having position vectors are collinear, whatever be .
22

Show that the points having position vector , and are collinear, whatever be .
23

Find a unit vector perpendicular to the plane ABC, where the points A, B, C, are , and respectively.
24

If and then find .
25

If , and , find .
26

If , and , find the angle between and .