Find the magnitude of the cross product of two orthogonal vectors aligned with the coordinate axes.

Vault Of Euclid

Magnitude of a Cross Product Using Properties

Vector spaces warmup

Use Properties of the Cross Product to find the magnitude of \(\mathbf{u} \times \mathbf{v}\), where \(\mathbf{u} = \langle -8, 0, 0 \rangle\) and \(\mathbf{v} = \langle 0, 2, 0 \rangle\).

The solution and a full step-by-step explanation are here. Sign in to read them.

What you need first

Standard basis vectors (i, j, k)
Basic properties of the cross product
Magnitude of a vector

What this problem tests

Tests the ability to apply scalar multiplication and geometric properties of the cross product rather than relying solely on the determinant formula.

This is a standard introductory problem in multivariable calculus or linear algebra, designed to test familiarity with the basic properties of the cross product.

Magnitude of a Cross Product Using Properties

What you need first

What this problem tests

More on Vector spaces