Question

find the magnitude and direction angle of v = -4i - 2j

Answer 1

This should ring some bells. \(|v| = \sqrt{(-4)^{2}+(-2)^{2}}\)

What about that direction?

Answer 2

i is the x direction, and j is the y direction.

Answer 3

If that was to be plotted on a standard x-y axis plane.

Answer 4

i solved the equation up above and I got sqrt of 20..don't know where to go from here

Answer 5

Ever hear of a "Reference Angle"?

Answer 6

Yes

Answer 7

What you solved above, that will give you the magnitude.

Answer 8

2 sqrt of 5 is the same as the sqrt of 20, yes?

Answer 9

Excellent. Thinking on a Right Triangle, pick an acute angle. Once you have done that, label the adjacent leg "4" and the opposite leg "2". Now what?

Answer 10

Yes, \(\sqrt{20} = 2\sqrt{5}\)

Answer 11

now i have to use the Pythagorean theorem to find the missing side?

Answer 12

If you would like, but it's quicker just to use the inverse tangent to find the reference angle you need.

Answer 13

I got 207 as the direction

Answer 14

Keep in mind that in a Right Triangle, we will get ONLY a reference angle. It's your responsibility to add 180º to get it into Quadrant III where it belongs.

Answer 15

Right, 206.565º