If the vectors a, b and c are coplanar, then `|{:(a, b, c),(a*a, a*b,a*c),(b*a,b*b,b*c):}|` is equal to

Options

A. 1
B. 0
C. `-1`
D. None of these 3

Answer

B

Explanation

Since, a, b and c are coplanar, there must exists three scalars c, y and z are not all zero such that
`xa+yb+zc=0" "…(i)`
Multiplaying both sides of Eq. (i) by a and b respectivelt, we get
`xa*aya*b+za*x=0" "...(ii)`
`ab(a+yb*b+zb*x=0" "...(ii)`
Eliminating x, y and z from Eqs. (i) ,(ii) and (iii), we get
`|{:(a,b,c),(a*a,a*b,a*c),(b*a,b*b,b*c):}|=0`