Vectors CYU

Vector is a quantity with:

• magnitude and direction

• magnitude

• direction

• none of the above

Given that the vector $\overrightarrow{OA}\ =\ \left(_{-3}^{\ \ 4}\right)$ , the magnitude of  $\left|3\ \overrightarrow{OA}\right|$  is


(a)  

Suppose 2 vectors, $\text{a}$ and $k\text{ a}$ , where $k$ is a constant. If the vectors are in opposite direction but of equal magnitude, what can you conclude about the value of $k$ ?

•  $k=1$  

•  $k>0\ \ \text{and}\ \ k\ne1$  

•  $k<0\ \text{ and }\ k\ne1$  

•  $k=-1$  

Which of the following vectors are parallel to  $\left(_{\ 3\ }^{\ 2}\right)$ ? Choose the answers that apply.

•  $\left(_{\ 4\ }^{\ 3}\right)$  
  

•  $\left(_{\ 6\ }^{\ 4}\right)$  
  

•  $\left(_{\ 1\ }^{\ 1}\right)$  
  

•  $\left(_{\ -1.5\ }^{\ \ \ -1}\right)$  

Each point in an octagon is labelled clockwise in the following order: A, B, C, D, E, F, G, H. Each side of the octagon is 1 unit long. Find the magnitude of:
 $\overrightarrow{AB}+\overrightarrow{BC}+\overrightarrow{CD}+\overrightarrow{DE}\$ 

 $+\ \overrightarrow{EF}+\overrightarrow{FG}+\overrightarrow{GH}+\overrightarrow{HA}$  

• 8 units
  

• 0 units
  

• The answer does not exist.
  

If a duck waddles from coordinate P = (-3, 2) to

Q = (6,5), then a vector that models the duck's motion is

• 〈-3,7〉

• 〈-9,3〉

• 〈9,-3〉

• 〈9,3〉

ABC is a triangle such that  $\overrightarrow{AB}\ =\ \left(_{-1}^{\ \ 5}\right)$  and  $\overrightarrow{AC}\ =\ \left(_{\ 8}^{-1}\right)$ . Calculate the length of BC.


(a)  

Given that  $\overrightarrow{PQ}\ =\ \left(_{3a}^{\ a}\right)$  and  $\left|PQ\right|=\frac{5\sqrt{10}}{2}$  , state the sum of the possible values of  $a$ .


(a)  

Given the coordinates of  $A=\left(-5,1\right)$  and  $B=\left(43,\ 38\right)$  , find  $\overrightarrow{AB}$ .

•  $\left(_{37}^{48}\right)$  

•  $\left(_{39}^{38}\right)$  

•  $\left(_{-37}^{-48}\right)$  

•  $\left(_{\ \ 39}^{-38}\right)$  

A is translated to B (5,-2) by  $\left(_{\ 7}^{-3}\right)$  . Find the sum of the x- and y- coordinates of A.

(a)