First slide

Vector triple product

Question

If $\vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \times \vec{b}) \times \vec{c}$ then

Moderate

A

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

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

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

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

Solution

$\begin{array}{l} \vec{a} \times (\vec{b} \times \vec{c}) = (\vec{a} \times \vec{b}) \times \vec{c} \\ or (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{a} \cdot \vec{b}) \vec{c} = (\vec{a} \cdot \vec{c}) \vec{b} - (\vec{c} \cdot \vec{b}) \vec{a} \end{array}$
$\begin{array}{l} or (\vec{a} \cdot \vec{b}) \vec{c} - (\vec{c} \cdot \vec{b}) \vec{a} = \vec{0} \\ or \vec{b} \times (\vec{c} \times \vec{a}) = \vec{0} \\ or (\vec{c} \times \vec{a}) \times \vec{b} = \vec{0} \\ or \vec{b} \times (\vec{c} \times \vec{a}) = (\vec{c} \times \vec{a}) \times \vec{b} = \vec{0} \end{array}$

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