Question

Given that P = (-5, 5) and Q = (-13, 6), find the component form and magnitude of 2vector PQ.

Answer 1

@mathstudent55 @TuringTest @asnaseer @Jhannybean

Answer 2

First find the vector \(\vec {PQ}\)

Answer 3

So if you wrote out your points as vectors, then you would have \[\vec {PQ} = <-13-5~,~ 6-5> = ~?\]

Answer 4

would the final vector be <-18, 1> ?

Answer 5

Good, now multiply each component by 2.

Answer 6

<-38, 2> right? and why would you multiply it by 2?

Answer 7

I meant <-36, 2> sorry

Answer 8

because you are trying to find a parallel vector, that is \(2\vec {PQ}\), to the vector \(\vec {PQ}\)

Answer 9

oh ok...where do I go from there then?

Answer 10

ooo wait is the magnitude sq. rt 325??:)

Answer 11

let's check, \[\sqrt{(-36)^2 +2^2} \ne \sqrt{325}\]

Answer 12

The magnitude is the square root of the vector components.\[\left|2\vec{PQ}\right| = \sqrt{(2\vec P)^2 +(2\vec Q)^2} = \sqrt{(-36)^2 +(2)^2}\]

Answer 13

:( those aren't any of my answer choices though
heres what it says
<-36, 2> , sqrt 325
<16, -2> , sqrt 65
<-16, 2> , sqrt130
<-16, 2> , sqrt 260

Answer 14

Oh I see where I went wrong.

Answer 15

The magnitude of the vector is just the distance of the vector. multiplying it by 2 just gives you a parallel vector. therefore if we found the magnitude of \(\vec{PQ}\) you would indeed get \(\sqrt{325}\).

Answer 16

oh ok :) thanks so much for your help:)

Answer 17

It's just \[2\left|\vec{PQ}\right| = 2\sqrt{(-18)^2 +(1)^2}\]