Let $\mathbf { v } = 7 \mathbf { j }$ and let $\mathbf { u }$ be a vector with length 5 that starts at the origin and rotates in the $x y$ - plane. Find the maximum value of the length of the vector $| \mathbf { u } \times \mathbf { v } |$.
A) $| \mathbf { u } \times \mathbf { v } | = 5$
B) $| \mathbf { u } \times \mathbf { v } | = 7$
C) $| \mathbf { u } \times \mathbf { v } | = 35$
D) $| \mathbf { u } \times \mathbf { v } | = 157$
E) $| \mathbf { u } \times \mathbf { v } | = 1$

Question

Quizplus · Accepted Answer

The magnitude of the cross product $| \mathbf { u } \times \mathbf { v } |$ is given by $| \mathbf { u } | | \mathbf { v } | \sin(\theta)$, where $\theta$ is the angle between $\mathbf { u }$ and $\mathbf { v }$. The maximum value occurs when $\sin(\theta) = 1$, i.e., $\theta = 90^\circ$. Thus, the maximum length is $5 \times 7 = 35$.

Let v=7j\mathbf { v } = 7 \mathbf { j }v=7j

Let $\mathbf { v } = 7 \mathbf { j }$