#
what is the angle between sum of the vectors and difference of two vectors

## Answers

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**Answer:**

Let the two vectors be

A

and

B

with magnitudes A and B respectively. Then magnitude of their sum is given by:

∣

A

+

B

∣=

A

2

+B

2

+2ABcosθ

→(1) (θ= angle between the vectors)

Magnitude of their difference is given by:

∣

A

−

B

∣=

A

2

+B

2

−2ABcosθ

→(2)

As ∣

A

+

B

∣=∣

A

−

B

∣

⇒A

2

+B

2

+2ABcosθ=A

2

+B

2

−2ABcosθ

⇒4ABcosθ=0 or cosθ=0

⇒θ=90

o

.

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