Question

10.2. Given : Pvector=A vector-B vector and P = A + B. The angle between A vector and B vector is -
(A) 0°
(B) 90°
(C)180°
(D) 270°
​

Answer 1

Answer:

0°

Explanation:

GIVEN :P = A+B and O= A - B

P and Q are seems to be a resultant vectors

SO ...

see the attached picture

Answer 2

Given:

The sum of vectors A and B = The difference between vectors A and B.

To Find:

The angle between vectors A and B.

Solution:

As given, P = A+ B ⇔ P = A - B

The vector of two vectors is equal to the vector difference.

The vector sum of A and B

P = √(A² + B² +2ABcosθ)

The vector difference of A and B.

P = √(A² + B² - 2ABcosθ)

Equating both above expressions.

⇒ √(A² + B² + 2ABcosθ) = √(A² + B² - 2ABcosθ)

⇒ 2AB cosθ = - 2AB cosθ

⇒  cosθ = - cosθ

⇒ 2 cosθ = 0

⇒ cos θ = 0

⇒ cos θ = 90°

Hence, the angle between vectors A and B is an option (B) 90°.