#### 15.2 Examples

For the following examples let us assume that we have a construction with points P1, P2, P3 and
P4 as well as vectors V1, V2 and V3.

- The expression ’V1+V2’ evaluates to a vector that is displayed in a row. ’v1+v2’ is
undefined. Be careful with lower- and uppercase letters!
- The expression ’V1ˆV2*V3 ’ is the scalar triple product of the vectors V1, V2 and V3.
- The expression V1 + V2*V3 is undefined because V2*V3 is a number whereas V1 is a
vector.
- The expression sqrt(V1*V1) evaluates to the length of V1. If you need the lenth of V1,
use ’Measure and calculate - Length’, it’s faster!
- The expression acos(V1*V2/(abs(V1)*abs(V2))) gives the angle between V1 and V2.

The image shows Archimedes used as a function-plotter for the function z = sin(x + y).