my teacher gave me this problems but i just can't figure out this one, please i really need to know this and if you can post Steps on how to do it will be awesome. Also i would rather see the procedure than a lot of explanation.

Given u=<3,4> w=<-2,2> and v=<-5,6> find the following:

u + v_____v - u_____4u - 3v_____||4u - 3v||

Also:

a unit vector in the direction of v

find the direction angle for -u

v*w (is v times w)

find the angle between v and w

show that the standard unit vectors i and j are orthogonal.

I know this long but i hope someone knows this answers, this is not homework to get points, I'm studying for a college test.