10.2 Vectors in 3D

Find the magnitude of  $\overrightarrow{v}$  with component form  $<4,5,2>$ . 

•  $3\sqrt{5}$  

•  $\sqrt{11}$  

•  $45$  

•  $11$  

Fill in the blank.
To find the unit vector  $\overrightarrow{u}$  in the direction of a given vector  $\overrightarrow{v}$ , divide  $\overrightarrow{v}$  by its ________________.

Calculate  $\overrightarrow{z}=3\overrightarrow{w}-2\overrightarrow{v}+\overrightarrow{u}$  given  $\overrightarrow{u}=<-1,3,2>$ ,  $\overrightarrow{v}=<1,-2,-2>$ , and  $\overrightarrow{w}=<5,0,-5>$ .

•  $<17,-4,11>$  

•  $<16,-1,13>$  

•  $<12,7,-9>$  

• none of these

Fill in the blank.

To find the unit vector in the opposite direction of a given vector, find the unit vector and multiply by _________.

Find the dot product of  $8\overrightarrow{i}+9\overrightarrow{j}-3\overrightarrow{k}$  and  $3\overrightarrow{i}-\overrightarrow{j}+5\overrightarrow{k}$ .

Fill in the blank.
(Round to the nearest hundredth.)
The angle between  $\overrightarrow{u}=<-1,3,0>$  and  $\overrightarrow{v}=<1,2,-1>$  is  ____ $\degree$  

Determine whether $\overrightarrow{u}=2\overrightarrow{i}-3\overrightarrow{j}+\overrightarrow{k}$ and $\overrightarrow{v}=-\overrightarrow{i}-\overrightarrow{j}-\overrightarrow{k}$  are parallel, orthogonal, or neither.

• parallel

• orthogonal

• neither

Use vectors to determine if the following points are collinear.  $\left(5,4,1\right)$ ,  $\left(7,3,-1\right)$ , and  $\left(4,5,3\right)$ .

• collinear

• not collinear