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