If \(\vec{a}\) and \(\vec{b}\) are non-zero vectors which are not parallel, then the angle between the vectors \(\vec{a}\times\vec{b}\) and \(\vec{b}\times\vec{a}\) is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\pi\)
The vector product is anticommutative:
\(\vec{b}\times\vec{a} = -(\vec{a}\times\vec{b})\)
Since \(\vec{a}\) and \(\vec{b}\) are non-zero and not parallel, \(\vec{a}\times\vec{b} \ne \vec{0}\).
So \(\vec{b}\times\vec{a}\) has the same magnitude as \(\vec{a}\times\vec{b}\) but the opposite direction. Two vectors in opposite directions make an angle of \(\pi\).
\( \displaystyle \cos\theta = \frac{(\vec{a}\times\vec{b})\cdot(-(\vec{a}\times\vec{b}))}{|\vec{a}\times\vec{b}|^2} = -1 \)
\(\theta = \pi\)