Meriam, Kraige & Bolton — Introduction to Dynamics: Problem 1_3

1/3 For the given vectors $\mathbf{V}_1$ and $\mathbf{V}_2$, determine $\mathbf{V}_1 + \mathbf{V}_2$, $|\mathbf{V}_1 + \mathbf{V}_2|$, $\mathbf{V}_1 - \mathbf{V}_2$, $\mathbf{V}_1 \times \mathbf{V}_2$, $\mathbf{V}_2 \times \mathbf{V}_1$, and $\mathbf{V}_1 \cdot \mathbf{V}_2$. Consider the vectors to be nondimensional. Given data from diagram: $\mathbf{V}_1$ has magnitude 12 at an angle of $30^\circ$ from the positive $x$-axis. $\mathbf{V}_2$ has magnitude 15 in the second quadrant, with a slope defined by a $3$-$4$-$5$ triangle (3 horizontal, 4 vertical).