If a, b, c are linearly independent vectors and `delta =|(a,b,c),(a.a,a.b,a.c),(a.c,b.c,c.c)|` then (a)`delta = 0` (b) `delta = 1` (C) A=any non-zero volue (d)None of these

Options

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

Answer

B

Explanation

Since a, b and c are coplanar, there must exist three scalars x,y and z not all zero such that
`ax+yb+zc=0" "…(i)`
ON multiplyaing both sids of Eq (i) by a and b respectively we get
`xaa+ya.b+za.c =0:" "…(ii)`
`ab.a+yb.b+zb.c=0" "...(iii)`
On eliminating x,y and z from Eqs, (i), (ii) and (iii), we get
`|{:(a,b,c),(a.a., a.b.,b.c),(b.a, a.b, b.c):}|=0`