Question

Given that P = (-5, 5) and Q = (-13, 10), find the component form and magnitude of 2 (line)PQ

<-16, 10>, sqrt(356)

<-36, 10>, sqrt(349)

<-16, 10>, sqrt(178)

<16, -10>, sqrt(89)

Answer 1

They are asking what is the vector with a tail at P and its head at Q ?

if you "slide" the vector so its tail is at (0,0), and find the location of its head, that will be the component form. in other words, calculate Q-P

the length will be the square root of the sum of its components squared
i.e. sqrt(x^2 + y^2)

Answer 2

Component form of a vector between two points:
<(x₂-x₁), (y₂-y₁)>

Magnitude of a vector between two points is the distance between them:
\[\sqrt{(y₂-y₁)² + (x₂-x₁)²}\]