3.2-06 Three-dimensional axis rotations

Three-dimensional axis rotations — linear algebra practice

Use right-handed axes, active rotations and column vectors to construct rotations about coordinate axes. Follow basis directions and concrete points, identify the fixed axis and compare successive turns about different axes. A final convention check explains why apparently conflicting formulas need careful interpretation.

What you will practise

• Apply the right-hand convention
• Construct axis rotation matrices
• Track fixed directions and ordered compositions

This microlearning belongs to Module 3 of the Complete Linear Algebra Course. Single-select and multiselect questions progress from interpretation to calculation, application and error diagnosis. Each problem is self-contained, and the explanations show how to justify a result rather than only identify a choice. In multiselect tasks, assess each statement separately; the number of correct choices varies.

Before starting, review planar rotations and three-coordinate vectors. Work through the reasoning on paper, compare your method with the explanation and revisit the assumptions behind any missed item. These skills prepare you to work with spatial graphics transforms.