Preview Activity 6.4.1.
Suppose we have a basis for consisting of the vectors
as shown in Figure 6.4.1. Notice that this basis is not orthogonal.
- Find the vector
that is the orthogonal projection of onto the line defined by - Explain why
is orthogonal to -
Define the new vectors
and and sketch them in Figure 6.4.2. Explain why and define an orthogonal basis forFigure 6.4.2. Sketch the new basis and - Write the vector
as a linear combination of and - Scale the vectors
and to produce an orthonormal basis and for