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Parametric Differentiation

For non-zero ...

Question

For non-zero vectors $\vec{a,} \vec{b} and \vec{c}$ the relation $|(\vec{a} \times \vec{b}) \cdot \vec{c}| = |\vec{a}| |\vec{b}| |\vec{c}|$ holds good, if
(a) $\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{c} = 0$

(b) $\vec{a} \cdot \vec{b} = 0 = \vec{c} \cdot \vec{a}$

(c) $\vec{a} \cdot \vec{b} = \vec{b} \cdot \vec{c} = \vec{c} \cdot \vec{a} = 0$

(d) $\vec{b} \cdot \vec{c} = \vec{c} \cdot \vec{a} = 0$

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a, b

c

a + b + c = 0

\vec{a,} \vec{b,} \vec{c}

(\vec{a} + \vec{b} + \vec{c}) . [(\vec{a} + \vec{b}) \times (\vec{a} + \vec{c})]

[\vec{a} \vec{b} \vec{c}]

2 [\vec{a} \vec{b} \vec{c}]

- [\vec{a} \vec{b} \vec{c}]

\to a, \to b, \to c, (\to a \times \to b) . \to c = ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣

\to a, \to b, \to c; ∣ ∣ ∣ (\to a \times \to b) \cdot \to c ∣ ∣ ∣ = ∣ ∣ \to a ∣ ∣ ∣ ∣ ∣ \to b ∣ ∣ ∣ ∣ ∣ \to c ∣ ∣

\to a, \to b

\to c

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