Practice Cross Product in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The cross product of two 3D vectors \mathbf{a} = \langle a_1, a_2, a_3 \rangle and \mathbf{b} = \langle b_1, b_2, b_3 \rangle is a new vector \mathbf{a} \times \mathbf{b} that is perpendicular to both \mathbf{a} and \mathbf{b}. Its magnitude equals the area of the parallelogram formed by \mathbf{a} and \mathbf{b}.
Place two arrows flat on a table. The cross product points straight up from the table, perpendicular to both. Its length tells you how much area the two arrows span—like the area of a parallelogram with the arrows as sides. If the arrows are parallel, they span no area, so the cross product is the zero vector.
Example 1
mediumFind \langle 1, 0, 0 \rangle \times \langle 0, 1, 0 \rangle.
Example 2
hardFind \langle 2, 3, 1 \rangle \times \langle 1, -1, 2 \rangle.
Example 3
mediumFind \langle 1, 2, 0 \rangle \times \langle 3, 0, 0 \rangle.
Example 4
easyIs \mathbf{a} \times \mathbf{b} = \mathbf{b} \times \mathbf{a}?