Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v.
-u = 4i, v = 3j
A) 4; 3k
B) 12; -k
C) 12; 12k
D) 12; k

Question

Quizplus · Accepted Answer

The magnitude of the cross product $u \times v$ is given by $|u \times v| = |u||v|\sin(\theta)$, where $\theta$ is the angle between $u$ and $v$. Since $u = 4i$ and $v = 3j$, they are perpendicular ($\theta = 90^\circ$), and $\sin(90^\circ) = 1$. Thus, $|u \times v| = |4||3|(1) = 12$. The direction of $u \times v$ is perpendicular to both $u$ and $v$, which in this case is along the $k$ axis (out of the $i-j$ plane). Since $u$ and $v$ form a right-handed system, $u \times v$ points in the positive $k$ direction, making the unit vector $k$.

Find the Magnitude of U × V and the Unit