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

Options

A. `A=3B`
B. `A=2B`
C. `A=B`
D. `B=2A`

Answer

C

Explanation

(c): Dot product of the sum and difference must be zero.
`(vecA+vecB).(vecA-vecB)=0`
`rArr vecA.vecA+vecB.vecA-vecA.vecB-vecB.vecB=0`
`vecA.vecB` is equal to `vecB. vecA`
`rArr vecA.vecA-vecB.vecB=0`
`rArr vecA.vecA-vecB.vecB=0`
`rArr A^(2)-B^(2)=0`
`rArr A=B`
Hence, option (c) is correct .