Answer to Question #110823 in Analytic Geometry for Hetisani Sewela

Question

Consider the vectors
u = (1, 0) and v = (0, 1).
7.1 Determine cos θ, where θ is the angle between u and v. (4)
7.2 Determine the area of the parallelogram determined by u and v.

Answer 1

$7.1. \\ \cos(\theta)=\cfrac{{\bf u}\cdot {\bf v}}{{\bf |u|}{\bf |v|}}=\cfrac{1\cdot 0 + 0\cdot 1}{\sqrt{1^2+0^2}\cdot \sqrt{0^2+1^2}}=0;\\ \quad \theta=\cfrac{\pi}{2}.\\ 7.2. \\S =|{\bf u}|\cdot|{\bf v}|\cdot\sin(\theta) =\\ \sqrt{1^2+0^2}\cdot \sqrt{0^2+1^2} \cdot 1=1$