230 m2p1 vector projection demo
Visual demonstration of vector projection
Below you will see a visual demonstration of the projection of vector onto the (nonzero) vector . This is denoted as and is itself a vector. (In the case of this applet, notice that lies along the x axis.)
You can think of as the shadow cast by onto . The goal is to determine how closely aligned these vectors are. In other words, how much of points in the same direction as ?
Please explore this further by moving the ♦ shapes at the end of each vector. This will automatically change the "shadow" of u onto v. Some questions to consider:
1. For what angle, , does point in the same direction as ?
2. For what angle, , does , point in the opposite direction as ?
3. For what angle, , is there no shadow at all? What does equal in this special case?