A cross b is equal to b Cross c show that A + C is equal to mB

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Solution

$\vec{a} \times \vec{b} = \vec{b} \times \vec{c} \vec{a} \times \vec{b} = - \vec{c} \times \vec{b} \vec{a} \times \vec{b} + \vec{c} \times \vec{b} = 0 (\vec{a} + \vec{c}) \times \vec{b} = 0 T h e r e f o r e (\vec{a} + \vec{c}) i s p a r a l l e l t o \vec{b} \vec{a} + \vec{c} = m \vec{b}, w h e r e m \in ℝ$

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A cross b is equal to b Cross c show that A + C is equal to mB

a→×b→=b→×c→a→×b→=-c→×b→a→×b→+c→×b→=0a→+c→×b→=0Therefore a→+c→ is parallel to b→a→+c→=mb→, where m∈ℝ