If the magnitudes of two vectors a and b are equal then which one of the following is correct?

Options

A. `(vec(a)+vec(b) ) ` is parallel to `(vec(a)-vec(b))`
B. `(vec(a)+vec(b))*(vec(a)-vec(b))=1`
C. `(vec(a)+vec(b))` is perpendicular to `(vec(a)-vec(b))`
D. None of the above

Answer

C

Explanation

Given `|vec(a)|=|vec(b)|`
Consider `(vec(a)+vec(b))*(vec(a)-vec(b))`
`=vec(a).vec(a)-vec(a).vec(b)+vec(b).vec(a)-vec(b).vec(b)`
`=|vec(a)|^(2)-|vec(b)|^(2)=|vec(a)|^(2)-|vec(a)|^(2)=0`
Hence `(vec(a)+vec(b))` is perpendicular to `(vec(a)-vec(b))`.