Question

x, y, z are distinct scalars such that [xa + yb + zc, xb + yc + za + zb] = 0, where vector(a, b, c) are non-coplanar vectors. Then

(a) x + y + z = 0

(c) xy + yz + zx = 0

(b) x3 + y3 + z3 = 0

(d) x2 + y2 + z2 = 0

Answer 1

Vector (a, b, c) are non-coplanar. Therefore,

But x, y, z are distinct.

Therefore,

x + y + z = 0