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.

• 887.47 feet

• 19.87 feet

• 19.38 feet

• 87.58 feet

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

•  $-3\overrightarrow{\ r\ }+\overrightarrow{\ s\ }\ -\overrightarrow{\ t\ }$  

•  $-3\overrightarrow{\ r\ }-\overrightarrow{\ s\ }-\overrightarrow{\ t\ }$  

•  $3\overrightarrow{\ r\ }+\overrightarrow{\ s\ }+\overrightarrow{\ t\ }$  

•  $3\overrightarrow{\ r\ }-\overrightarrow{\ s\ }+\overrightarrow{\ t\ }$  

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

•  $<1.5,\ 1.1>$  

•  $<1.1,\ 1.5>$  

•  $<-7.1,\ -0.7>$  

•  $<-7.1,\ -1.1>$  

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

• 3.46

• 7.13 

• 1.86

• 7.18

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

•  $<-1,\ -8.8,\ 1>$  

•  $<1,\ 8.8,\ -1>$  

•  $<1.8,\ -9.4,\ 15.4>$  

•  $<-1.8,\ 9.4,\ -15.4>$  

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

• 12.33

• 8.91

• 8.80

• 18.13

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  $\overrightarrow{\ v\ }=<\frac{3}{8},\ -2>$ .

•  $<\frac{1}{4},\ 7>$  

•  $<-\frac{5}{4},\ 7>$  

•  $<\frac{5}{4},\ -1>$  

•  $<-\frac{1}{4},\ 4>$  

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  $\overrightarrow{\ z\ }=<-\frac{1}{2},\ \frac{3}{4},\ -\frac{1}{6}>$ .

•  $<\frac{7}{2},\ 0,\ \frac{4}{5}>$  
  

•  $<\frac{25}{8},\ 0,\ \frac{4}{5}>$  
  

•  $<\frac{7}{2},\ 0,\ \frac{6}{5}>$  
  

•  $<\frac{7}{2},\ \frac{33}{8},\ \frac{4}{5}>$  
  

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

•  $\frac{27}{4}\overrightarrow{\ i\ }-14\overrightarrow{\ j\ }-\frac{1}{15}\overrightarrow{\ k\ }$  

•  $9\overrightarrow{\ i\ }+\frac{89}{20}\overrightarrow{\ j\ }-\frac{93}{4}\overrightarrow{\ k\ }$  

•  $\frac{21}{4}\overrightarrow{\ i\ }-14\overrightarrow{\ j\ }-\frac{1}{15}\overrightarrow{\ k\ }$  

•  $\frac{27}{4}\overrightarrow{\ i\ }-14\overrightarrow{\ j\ }+\frac{1}{15}\overrightarrow{\ k\ }$  

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?

• 7.5 mph

• 17.3 mph

• 30.0 mph

• 26.0 mph