Cross product practice problems

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -1, 0, 1 \rangle,\ \mathbf{v} = \langle -2, 4, 1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 3, -2, 3 \rangle,\ \mathbf{v} = \langle 4, 0, -3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 3, 4, -3 \rangle,\ \mathbf{v} = \langle -1, -3, 2 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 4, -1, -2 \rangle,\ \mathbf{v} = \langle -1, 2, -1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 3, 3, -1 \rangle,\ \mathbf{v} = \langle 0, -1, 0 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 2, 1, 1 \rangle,\ \mathbf{v} = \langle -1, -4, -1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -3, 0, 2 \rangle,\ \mathbf{v} = \langle -2, -1, 2 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -4, 3, 0 \rangle,\ \mathbf{v} = \langle 4, -1, 3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 3, 2, -4 \rangle,\ \mathbf{v} = \langle -4, 2, 1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 0, -4, -2 \rangle,\ \mathbf{v} = \langle 2, -2, 1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -2, 0, 3 \rangle,\ \mathbf{v} = \langle 3, 1, -1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 0, -2, 1 \rangle,\ \mathbf{v} = \langle 4, 3, 1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -2, -3, 0 \rangle,\ \mathbf{v} = \langle 3, 1, -3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -1, 3, 0 \rangle,\ \mathbf{v} = \langle 0, 2, 3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 1, -3, 2 \rangle,\ \mathbf{v} = \langle 2, 1, -3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 0, 0, 1 \rangle,\ \mathbf{v} = \langle 2, 2, -3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -1, 2, -2 \rangle,\ \mathbf{v} = \langle 2, -4, -4 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 2, 2, 3 \rangle,\ \mathbf{v} = \langle -4, -3, -1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -4, -3, 3 \rangle,\ \mathbf{v} = \langle -1, -4, 4 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -2, -2, 2 \rangle,\ \mathbf{v} = \langle 0, 1, 0 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 4, -2, 4 \rangle,\ \mathbf{v} = \langle -4, 4, 2 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -3, -1, -4 \rangle,\ \mathbf{v} = \langle -1, -2, -1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -3, 2, 2 \rangle,\ \mathbf{v} = \langle -2, -1, -3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -2, 3, 3 \rangle,\ \mathbf{v} = \langle 4, 2, 0 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -4, 2, 1 \rangle,\ \mathbf{v} = \langle 3, 0, -3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 1, 1, 2 \rangle,\ \mathbf{v} = \langle 4, 1, -4 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 2, 2, 2 \rangle,\ \mathbf{v} = \langle -4, -3, -3 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 3, 1, 1 \rangle,\ \mathbf{v} = \langle -4, 4, 2 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle 1, 4, 3 \rangle,\ \mathbf{v} = \langle -3, -4, -1 \rangle \), and the area of the parallelogram they span.

Find \( \displaystyle \mathbf{u} \times \mathbf{v} \) for \( \displaystyle \mathbf{u} = \langle -1, 3, 1 \rangle,\ \mathbf{v} = \langle 4, -1, -2 \rangle \), and the area of the parallelogram they span.