1. Construct a right-handed $\mathbb{R}^3$ reference system with axes X, Y and Z and
then draw a box in the reference system to indicate the position of the
point $P = (1, -3, 2) \in \mathbb{R}^3$ and, finally, draw $\overrightarrow{OP}$ and determine the mag-
nitude and the direction angles of the directed line segment $\overrightarrow{OP}$. [10]
2. Let $\vec{a}, \vec{b} \in \mathbb{R}^2$ be vectors such that $\vec{a}, \vec{b} \neq \vec{0}$. Use vector geometric to
show that for $\vec{a} \uparrow \downarrow \vec{b}$, $-(\vec{a} - \vec{b}) = -\vec{a} + \vec{b}$.
[5]
