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if axxb = bxxc != 0 with a != -c then sh...

if `axxb = bxxc != 0` with a `!= -c` then show that a+c = kb, where k is scalar.

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To solve the problem, we need to show that if \( \mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} \neq 0 \) and \( \mathbf{a} \neq -\mathbf{c} \), then \( \mathbf{a} + \mathbf{c} = k\mathbf{b} \) for some scalar \( k \). ### Step-by-step Solution: 1. **Start with the given equation:** \[ \mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{c} \] ...
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