Given that P = (-1, 8), Q = (-3, 3), R = (9, -9), and S = (13, -8), how do you find the component form and magnitude of the vector PQ + 3RS?

1 Answer
Jim G.
May 26, 2017

((10),(-2)),2sqrt26

Explanation:

vec(PQ)=ulq-ulp

color(white)(vec(PQ))=((-3),(3))-((-1),(8))=((-2),(-5))

vec(RS)=uls-ulr=((13),(-8))-((9),(-9))=((4),(1))

3vec(RS)=3((4),(1))=((12),(3))

rArrvec(PQ)+3vec(RS)

=((-2),(-5))+((12),(3))=((10),(-2))larrcolor(red)" in component form"

|vec(PQ)+3vec(RS)|=sqrt(10^2+(-2)^2)=2sqrt26

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