If , , are three non-zero vectors, then which of the following statement (s) is/are…

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

Problem

\mathbf{a}

\mathbf{b}

\mathbf{c}

are three non-zero vectors, then which of the following statement (s) is/are true? (1)

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

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

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

form a right handed system (2)

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

\mathbf{a} \times \mathbf{b}

form a right handed system (3)

\mathbf{a} \cdot \mathbf{b} + \mathbf{b} \cdot \mathbf{c} + \mathbf{c} \cdot \mathbf{a} < 0

, if

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

(4)

\frac{(\mathbf{a} \times \mathbf{b}) \cdot (\mathbf{b} \times \mathbf{c})}{(\mathbf{b} \times \mathbf{c}) \cdot (\mathbf{a} \times \mathbf{c})} = -1

, if

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