Part A
Given that P=(5,4), Q=(7,3), R=(8,6), and S=(4,1), find the component form of the vector PQ+3RS.
a. <10,16>****
b. <6,4>
c. <2,6>
d. <14,14>
Part B
Use the information from Part A to find the magnitude of the vector PQ+3RS.
a. 356
b. sqrt(26)
c. 2*sqrt(10)
d. 2*sqrt(89)
I know that Part A is correct, but I do not understand how to find the magnitude.

a. PQ=(75)x+(34(y)=2 ,1
RS=(48)x+(16)y=4,5
PQ+3RS=2 ,1 +3( 4,5)=(214,115)=10,16
magnitude= sqrt(10^2+(16)^2)=sqrt(356)
factoring 356
2*178
2*2*89
magnitude=2sqrt(89)

In general if you have points P(a,b) and Q(c,d)
then vector PQ = <ca , db>
Notice I went from P to Q, so the subtraction is "destination x  starting x" , same for the y
Then to get vector QP we would get <ac, bd>
for yours, PQ = <75, 34> = <2,1>
to find the magnitude of vector <x,y> find √( x^2 + y^2)
e.g. PQ = √(2^2 + (1)^2 ) = √5
since your part a) is correct simply follow the above rule, I can see the answer

I would also appreciate if someone could better explain how to get Part A because my teacher did not explain this very well.