SME
Grade 12 Math
Vectors in three dimensions: dot and cross products
The main lesson, then each kind of problem it solves.
Vectors in three dimensions: dot and cross products
Main lesson
The cross product
Use this for “Find u × v for u = ⟨1, 2, 3⟩ and v = ⟨2, 0, 1⟩, and the areas of the parallelogram and the triangle with sides u and v from one vertex.”
Volume from the triple product
Use this for “Find the volume of the box that u = ⟨1, 2, 0⟩, v = ⟨0, 1, 3⟩ and w = ⟨2, 0, 1⟩ span.”
Distance and midpoint in space
Use this for “Find the distance between P(1, 2, 3) and Q(3, 5, 9) and the midpoint of PQ.”