If `vec(a) and vec(b)` are two unit vectors, then the vector `(vec(a) + vec(b)) xx (vec(a) xx vec(b))` is parallel to

Options

A. All three vectors must be parallel
B. `vec(b) and vec(c)` must be parallel to each other, but `vec(a)` need not be parallel to `vec(b) and vec(c)`
C. `vec(a) and vec(b)` must be perpendicular to each other
D. It is impossible for three non-zero vectors `vec(a), vec(b) and vec(c)` to have the property stated above

Answer

D

Explanation

Initially `a+b=c`
when `3a+ 2b= 2c`
`because c= a+b`
`therefore 3a+ 2b= 2(a+b) rArr a= 0`
Hence it is impossible for three non-zero vectors to have the property stated above