Which one of the following is correct ? If the vector `vec(c)` is normal to the vectors `vec(a) and vec(b)`, then `vec(c)`, is :

Options

A. parallel to both `vec(a)+vec(b) and vec(a)-vec(b)`
B. `vec(a)-vec(b) and` parallel to `vec(a)+vec(b)`
C. normal to `vec(a)+vec(b) ` and parallel to `vec(a)-vec(b)`
D. normal to both `vec(a)+vec(b) and vec(a)-vec(b)`

Answer

D

Explanation

As given
`vec(c)`, is normal to the vectors `vec(a) and vec(b)`
`rArr vec(c).vec(a) = 0 and vec(c).vec(b)=0`
`rArr vec(c).(vec(a)+vec(b))=vec(c).vec(a)+vec(c).vec(b)=0`
`rArr ` Also`vec(c). (vec(a)-vec(b))=vec(c).vec(a)-vec(c).vec(b)=0`
`vec(c)` is normal to `vec(a)+vec(b) and vec(a)-vec(b)`.