Question:
The position vectors of three points A, B and C are ab . and c respectively, where, ca b (cos )( sin) .22 What is () () ()ab bc ca () () ()ab bc ca equal to?
The position vectors of three points A, B and C are ab . and c respectively, where, ca b (cos )( sin) .22 What is () () ()ab bc ca () () ()ab bc ca equal to?
Options:
- a) o
- b) 2c
- c) 3c
- d) unit vector
- a) o
- b) 2c
- c) 3c
- d) unit vector
correct answer : a)
Explanation:
ab bc ca
×() +×() +×()
= ab ba c
×() +×() ×
= ab ba ab
×() +×() ×+()coss in22θθ
= ab ba ab
×() +× () -× ()coss in22θθ
= ab ab ab
×() -× () -× ()coss in22θθ
= ab
×() -+()
1
22coss inθθ = 0
ab bc ca
×() +×() +×()
= ab ba c
×() +×() ×
= ab ba ab
×() +×() ×+()coss in22θθ
= ab ba ab
×() +× () -× ()coss in22θθ
= ab ab ab
×() -× () -× ()coss in22θθ
= ab
×() -+()
1
22coss inθθ = 0