Question

What is the magnitude and direction of GH if G(3, -2) and H(6, 4)?

magnitude: 6.71 units; direction 63.43°

magnitude: 6.71 units: direction: 26.57°

magnitude: 3.61 units; direction: 26.57°

magnitude: 3.61 units: direction: 63.43°

Answer 1

first find the resultant vector
what is it?

Answer 2

im not sure what that is

Answer 3

it's the same thing you just did; subtract the final coordinates from the initial ones

Answer 4

v=<xh-xg,yh-yg>

Answer 5

oh right, i thought this was solved a different way.

Answer 6

we will have to do more, but the first step is finding the vector components

Answer 7

ok, the components are <3,6>

Answer 8

ok, so the magnitude (length) for a vector is found using the pythagorean theorem on its components

Answer 9

could i use the distance formula?

Answer 10

\[\vec v=\langle x,y\rangle\]the magnitude is\[\|\vec v\|=\sqrt{x^2+y^2}\]

Answer 11

if that is what you mean by the distance formula (hopefully you can see how they are related)

Answer 12

and for the angle we use a little trigonometry
I presume you have taken or are taking trig, right?

Answer 13

this is actually geometry

Answer 14

how to calculate the angle ?

Answer 15

I know to calculate the angle with trig\[\tan\theta=\frac yx\implies\theta=\tan^{-1}\frac yx\]but with pure geometry I guess we have to do some reasoning about the fact that the y component is twice as long as the x component

Answer 16

which trig function would we use for this?

Answer 17

tangent, (which leads to inverse tangent) as I wrote above

Answer 18

ok, i got the magnitude. 6.71