IF ` vecA xx vecB =vecC xx vecD and vecA xx vecC = vecB xx vecD + ` while ` | vecA| ne |vecD| | vecB| ne | vecC|` show `( vecA - vecD )` that and ` ( vecB - vecC)` are parallel

Explanation

To show that the vectors \( \vec{A} - \vec{D} \) and \( \vec{B} - \vec{C} \) are parallel, we start with the given equations:

1. \( \vec{A} \times \vec{B} = \vec{C} \times \vec{D} \)
2. \( \vec{A} \times \vec{C} = \vec{B} \times \vec{D} \)

We need to prove that \( (\vec{A} - \vec{D}) \) and \( (\vec{B} - \vec{C}) \) are parallel, which means we need to show that:

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