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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 equations:** We know that: \[ \mathbf{A} \times \mathbf{B} = \mathbf{B} \times \mathbf{C} ...
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