If is perpendicular to

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

Problem

\mathbf{a} \times (\mathbf{b} \times \mathbf{c})

is perpendicular to

(\mathbf{a} \times \mathbf{b}) \times \mathbf{c}

, we may have (1)

(\mathbf{a} \cdot \mathbf{c})|\mathbf{b}|^2 = (\mathbf{a} \cdot \mathbf{b})(\mathbf{b} \cdot \mathbf{c})

(2)

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

(3)

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

(4)

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