I did the rest of a problem right.. It asks to determine whether the parallelogram is a rectangle, meaning right angles..
A(2,-1,4), B(3,1,2), C(0,5,6), D(-1,3,8)
cos theta = dot product of u and v divided by magnitude of u and v
The Attempt at a Solution
I drew a sketch parallelogram, with A at Northwest, B at NE, C at SE, and D at SW..
I got vector AD and BC to be <-3,4,4> and vectors AB and DC to be <1,2,-2>
mag of AB/BC is square root 41, etc. if you can help me, you should know how I got there.
cos theta = [(-3*1) +(4*2) + (4*-2)]/[square root of 41*square root of 9]
[-3]/[square root 369]=cos theta
The back of my book says 81.02 degrees..