Unit 5 · 6 lessons
Vectors
Quantities with a direction: describe them three ways, add and scale them, write them as components in 2-space and 3-space, steer planes through the wind, and multiply them with the dot and cross products.
- 56 practice questions
- 45 flashcards
- 2 interactive lessons
Lessons
- 1Vectors, Scalars and DirectionA vector carries a size AND a direction. Learn the notation, when two vectors are equal or opposite, and the three ways to state a direction: a standard angle, a true bearing and a quadrant bearing.9 questions
- 2Adding, Subtracting and Scaling VectorsAdd vectors tip to tail or as a parallelogram, subtract by adding the opposite, stretch with scalars, find magnitudes with the cosine law, and simplify vector expressions using the same properties as ordinary algebra.Interactive9 questions
- 3Cartesian Vectors in 2-Space and 3-SpaceWrite a vector as a list of components, convert between magnitude-and-direction form and components, plot points and vectors in three dimensions, and add, subtract and scale vectors one component at a time.9 questions
- 4Applications: Forces, Wind and CurrentCombine forces into a resultant and find the equilibrant that balances it, then solve navigation problems: an airplane in a wind and a boat in a current, using components or the cosine and sine laws.10 questions
- 5The Dot ProductMultiply two vectors to get a scalar that measures how much they point the same way. Use it to find angles, test for perpendicular vectors, project one vector onto another, and calculate work.Interactive9 questions
- 6The Cross ProductMultiply two vectors in 3-space to get a third vector perpendicular to both. Its direction follows the right-hand rule and its length gives areas, torques and, with the dot product, volumes.10 questions