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If for two vector vecA and vecB, sum (ve...

If for two vector `vecA` and `vecB`, sum `(vecA+vecB)` is perpendicular to the difference `(vecA-vecB)`. The ratio of their magnitude is

A

1

B

2

C

3

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
`(vecA+vecB)` is perpendicular to `(vecA-vecB)` Thus
`(vecA+vecB).(vecA-vecB)=0`
or `A^(2)+vecB.vecA-vecA.vecB-vecB^(2)=0`
Bacause fo commutative property of dot product `vecA.vecB=vecB.vecA`
`A^(2)-V^(2)=0` or `A=B`
Thus the ratio of magnitudes `(A)/(B)=1`
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