Quiz 6: Dot Product

If  $u\cdot v=0$  , then u and v are perpendicular

• True

• False

• Not enough information

Let $u=4i-5j$  and $v=-2i-3j$  

Find $u\cdot v$  

•  $23$  

•  $-7$  

•  $7$  

•  $-23$  

Let  $u=i+j$  and  $v=-i+j$  

Find the angle between u and v.

•  $45\degree$  

•  $60\degree$  

•  $135\degree$  

•  $90\degree$  

Let $u=\frac{3}{2}i-\frac{3}{2}j$  and  $v=2i$  

What is the projection of u onto v? $\operatorname{proj}_vu$  

•  $<\frac{3}{2},\ \frac{3}{2}>$  

•  $<3,\ 0>$  

•  $<\frac{3}{2},\ 0>$  

•  $<-\frac{3}{2},\ -\frac{3}{2}>$  

Which of the following vectors describe a 5-Ib force acting in the direction of  $u=<3,\ 2>$  

•  $<\frac{3}{\sqrt{13}},\ \frac{2}{\sqrt{3}}>$  

•  $<\frac{15}{\sqrt{13}},\ \frac{10}{\sqrt{13}}>$  

•  $5<3,\ 2>$  

•  $\frac{5}{13}<3,\ 2>$  

Let $u=<5,\ 4>$  and  $v=<\frac{5}{2},\ 2>$  

Determine whether u and v are...

• Parallel

• Orthogonal

• Neither

• Insufficient information

Which of the following points corresponds to  $t=-1$  in the parametrization  $x=t^{2\ }-4$  ,  $y=t+\frac{1}{t}$  ?

•  $\left(-3,\ 0\right)$  

•  $\left(-3,\ -2\right)$  

•  $\left(-5,-2\right)$  

•  $\left(-5,\ 0\right)$