Discussion
Let \(\vec{a}\), \(\vec{b}\) be two distinct vectors that are not parallel. The vector \(\vec{c} = \vec{a} \times \vec{b}\) is
Answer: C
The vector \(\vec{c}\) is orthogonal to \(\vec{a} + \vec{b}\).
A cross product is perpendicular to both of its factors: \(\vec{c}\cdot\vec{a} = 0\) and \(\vec{c}\cdot\vec{b} = 0\). Adding these gives \(\vec{c}\cdot(\vec{a} + \vec{b}) = 0\), so \(\vec{c}\) is orthogonal to the sum, and indeed to every vector in the plane of \(\vec{a}\) and \(\vec{b}\).
\(\vec{c}\) is not zero, because a cross product vanishes only when the vectors are parallel (or one of them is zero), and these are not. The two 'alone' options are wrong because \(\vec{c}\) is orthogonal to both vectors, not to one of them only.
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