Analysis: Vectors

The vector $\overrightarrow{\ v\ }$  has a magnitude of 89.7 feet and a direction of  $12\degree\ 48'$ . Find the magnitude of its vertical component.

What is an expression for $\overrightarrow{\ x\ }$ involving  $\overrightarrow{\ r\ }$ ,  $\overrightarrow{\ s\ }$ , and  $\overrightarrow{\ t\ }$ ?

Find the ordered pair that represents the vector from $A\left(-4.3,\ -0.9\right)$  to  $B\left(-2.8,\ 0.2\right)$ .

Given $A\left(-4.3,\ -0.9\right)$  and  $B\left(-2.8,\ 0.2\right)$ , find the magnitude of  $\overrightarrow{AB}$ . 

Find the ordered triple that represents the vector from $A\left(-1.4,\ 0.3,\ -7.2\right)$ to $B\left(0.4,\ -9.1,\ 8.2\right)$ .

Given $A\left(-1.4,\ 0.3,\ -7.2\right)$ and $B\left(0.4,\ -9.1,\ 8.2\right)$ , find the magnitude of  $\overrightarrow{AB}$ .

Find an ordered pair to represent $\overrightarrow{\ u\ }$ in $\overrightarrow{\ u\ }=\frac{3}{4}\overrightarrow{\ w\ }-2\overrightarrow{\ v\ }$   if   $\overrightarrow{\ w\ }=<-\frac{2}{3},\ 4>$  and  $\overrightarrow{\ v\ }=<\frac{3}{8},\ -2>$ .

Find an ordered triple to represent $\overrightarrow{\ x\ }$ in $\overrightarrow{\ x\ }=-6\overrightarrow{\ z\ }+\frac{1}{4}\overrightarrow{\ y\ }$   if   $\overrightarrow{\ y\ }=<2,\ 18,\ -\frac{4}{5}>$  and  $\overrightarrow{\ z\ }=<-\frac{1}{2},\ \frac{3}{4},\ -\frac{1}{6}>$ .

Write $\overrightarrow{MN}$ as the sum of unit vectors for  $M\left(-\frac{3}{4},\ 5,\ \frac{2}{3}\right)$ and  $N\left(6,\ -9,\ \frac{3}{5}\right)$ . 

During a weekend surfboard competition, Kiyoshi moves at a $30\degree$  angle toward the shore. The velocity component toward the shore is 15 mph. What is Kiyoshi's velocity?