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If where , and are non-zero vectors, then prove that either or and are parallel.
If $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$ where $\vec{a}$, $\vec{b}$ and $\vec{c}$ are non-zero vectors, then prove that either $\vec{b} = \vec{c}$ or $\vec{a}$ and $(\vec{b} - \vec{c})$ are parallel.
Given: $\vec{a} \times \vec{b} = \vec{a} \times \vec{c}$
To show: $\vec{b} = \vec{c}$ or $\vec{a}$ and $(\vec{b} - \vec{c})$ are parallel
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From ISC 2024 Mathematics Paper 1, question 16(i).