3Blue1Brown: Linear Algebra Chapter 10: Cross Products - Quiz

Cross products and orientation

Study the geometric ideas from 3Blue1Brown’s Chapter 10, Cross products, with selected connections to its follow-up lesson on linear transformations and duality.

Topics

• The distinction between a planar signed-area determinant and a three-dimensional vector cross product.
• Orientation, right-hand conventions, zero products and collinearity.
• Parallelogram areas, fixed-length angle changes and scaling one or both inputs.
• Anticommutativity through column swaps and reversal of the normal direction.
• The symbolic cofactor mnemonic and its connection with the scalar triple product and dot-product duality.
• Linear maps taking the unit square to a parallelogram.

Preparation

Review vectors, determinants and basic trigonometry. Distinguish signed quantities from non-negative geometric areas and use an ordered coordinate basis when reasoning about orientation. Some items require selecting several statements. The lesson reference above supplies context for questions about the video’s exposition; the optional follow-up on duality develops the deeper computational connection.