SME
Grade 12 Math
Vectors: components, magnitude and dot product
The main lesson, then each kind of problem it solves.
Vectors: components, magnitude and dot product
Main lesson
Adding vectors
Use this for “Find u + v for u = ⟨3, 1⟩ and v = ⟨1, 2⟩, and its magnitude.”
A scalar times a vector
Use this for “Find −2u for u = ⟨3, 4⟩ and its magnitude.”
The dot product and the angle between vectors
Use this for “Find the angle between ⟨2, 1⟩ and ⟨1, 3⟩” or “Are these vectors perpendicular?”
The resultant of two forces
Use this for “Forces of 30 N at 0° and 40 N at 60° pull on a ring. Find the resultant.”