Vector as a magnitude and direction

[brandy]

Hello,

My math teacher is sick and the sub can't explain this problem.

If vector u = 12 units at 60 degrees and vector v = 8 units at 310 degrees, find the sum of vectors u and v as:

a) a sum of two components which I can do using sohcahtoa (12cos60 = x, 12sin60 = y) and (8cos50 = x, 8 sin 50 = y) therefore after a little more math I got 11.14i + 4.26j.

my problem is this

b) a magnitude and direction????

we have been using law of cosines for everything so I assume I can use it for the magnitude , but when I do I use angle 110 degrees and the book says to use 70 degrees??? why????

I am clueless on why they use tan (theta) = 4.26/11.14 also.

My visuals from class use a diagram with the two vectors drawn on a cartesian coordinate system (vector u in quadrant 1 and vector v in quadrant 4) so wouldn't the resultant vector connect vectors u and v from top to bottom?

I am soooooo confused on this??? and I'm not usually so dumb. Please help me

 

[skeeter]

vector u = 12 units at 60 degrees and vector v = 8 units at 310 degrees, find the sum of vectors u and v

using components ...

let u + v = r

\(\displaystyle u_x + v_x = r_x\)

\(\displaystyle 12\cos(60) + 8\cos(310) = r_x\)

\(\displaystyle u_y + v_y = r_y\)

\(\displaystyle 12\sin(60) + 8\sin(310) = r_y\)

\(\displaystyle |r| = \sqrt{r_x^2 + r_y^2} \approx 11.9\)

direction of r ...

\(\displaystyle \theta = \arctan\left(\frac{r_y}{r_x}\right) \approx 21^{\circ}\)

 

[brandy]

I understand how to get everything except the direction. Why and how is it set up?

 

[skeeter]

\(\displaystyle \tan{\theta} = \frac{opposite}{adjacent} = \frac{r_y}{r_x}\)

to get \(\displaystyle \theta\) , use the inverse tangent function.

 

[brandy]

I understand how trig function work and how to solve them, but I don't understand the diagram and why to use that set up on this problem.

 

[skeeter]

look at this diagram ... if you are still having problems understanding the method of vector addition using components, then I recommend you do some research on your own til you find an explanation that works for you.

 

[brandy]

Thank you.