\langle 1, 0, 4 \rangle \times \langle 2, -1, 3 \rangle = \langle (0)(3) - (4)(-1), -[(1)(3) - (4)(2)], (1)(-1) - (0)(2) \rangle = \langle 0 + 4, -(3 - 8), -1 - 0 \rangle = \langle 4, 5, -1 \rangle

Wed, 06 May 2026 02:52:49 +0000

Understanding Cross Products in 3D Space: A Step-by-Step Calculation of ⟨1, 0, 4⟩ × ⟨2, −1, 3⟩ The cross product of two vectors in three-dimensional space is a fundamental operation in linear algebra, physics, and engineering. Despite its seemingly abstract appearance, the cross product produces another vector perpendicular to the original two. This article explains how to compute the cross product of the vectors ⟨1, 0, 4⟩ and ⟨2, −1, 3⟩ using both algorithmic step-by-step methods and component-wise formulas—ultimately revealing why ⟨1, 0, 4⟩ × ⟨2, −1, 3⟩ = ⟨4, 5, −1⟩. --- ### What Is a Cross Product?