Calculus III: The Dot Product (Level 9 of 12)

The video tutorial covers three examples to demonstrate how to compute scalar, vector, and orthogonal projections. The first example involves finding these projections of vector b onto vector a, using dot products and unit vectors. The second example extends this to vectors u and v in space, emphasizing careful notation. The final example involves finding a vector b with a specific scalar projection onto vector a. Each example illustrates the process of calculating projections and verifying orthogonality.

What components of vector b are orthogonal to one another?

Explain how to find the scalar projection of vector u onto vector v.

If vector a equals 3, 0, negative 1, how would you find a vector b such that its components along vector a equal 2?