Question

Find the magnitude & direction of the vector JK given points J(1,0) & K(-2,3).

Answer 1

Magnitude = length of the line-segment
= distance between J and K
= sqrt( (1-(-2)) ^ 2 + (0 - 3)^2 ) (using distance between 2 points formula)
= sqrt( 3^2 + 3^2 ) = sqrt(18)
= 3 *sqrt(2)

To get the direction, a quick way is:
tan (angle) = (difference of y-coordinates) / (difference of x-coordinates)
= (0 - 3) / (1 - (-2))
= -3/3 = -1
tan 45 = 1
but since we have -1, we subtract 45 from 180 to get 135
so direction is 135 from 'positive horizontal'.

If you want, I could explain why we subtract from 180 if the tan is negative, and why use tan at all here.

Answer 2

im interested to know why they subtract 180...i often get confused whether to subtract 180 or add 360 or whatever :/

Answer 3

I think I get it now, thank you!(:

Answer 4

welcome @shanti99