If and are distinct scalars such that where and are non-coplanar vectors

MATHEMATICS · Single correct · CBSE · Mathematics · Vector Algebra · Vector Algebra

Problem

x, y

and

z

are distinct scalars such that

[x\mathbf{a} + y\mathbf{b} + z\mathbf{c}, x\mathbf{b} + y\mathbf{c} + z\mathbf{a}, x\mathbf{c} + y\mathbf{a} + z\mathbf{b}] = 0

where

\mathbf{a}, \mathbf{b}

and

\mathbf{c}

are non-coplanar vectors, then (1)

x + y + z = 0

(2)

xy + yz + zx = 0

(3)

x^3 + y^3 + z^3 = 0

(4)

x^2 + y^2 + z^2 = 0