For non-zero vectors

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

Problem

\mathbf{a}, \mathbf{b}, \mathbf{c}

|\mathbf{a} \times \mathbf{b} \cdot \mathbf{c}| = |\mathbf{a}||\mathbf{b}||\mathbf{c}|

holds if and only if (1)

\mathbf{a} \cdot \mathbf{b} = 0, \mathbf{b} \cdot \mathbf{c} = 0

(2)

\mathbf{b} \cdot \mathbf{c} = 0, \mathbf{c} \cdot \mathbf{a} = 0

(3)

\mathbf{c} \cdot \mathbf{a} = 0, \mathbf{a} \cdot \mathbf{b} = 0

(4)

\mathbf{a} \cdot \mathbf{b} = \mathbf{b} \cdot \mathbf{c} = \mathbf{c} \cdot \mathbf{a} = 0