How can I solve this using dot product?

Question

1. Find angle BAC if A = (2, 2, 2), B = (4, 2, 1), and C = (2, 3, 1).

I have no idea how to draw the points on a 3 coordinate system.

Answer 1

BAC is the angel produce by vector AB & AC

so

AB=B-A= (4,2,1)-(2,2,2)=(2,0,-1)

AC=C-A=(4,2,1)-(2,3,1)=(2,-1,0)

&

Angel BAC=arccos( (AB.AC)/(|AB|*|AC|) )

=arccos( (4+0+0)/(square(5)*square(5)) )

=arccos(4/5)

=36.87

Answer 2

cos Θ = AB 'dot' AC / [ |AB||AC| ]..AB = < 2,0,-1> & AC = < 0,1,-1>...about 1.25 radians...you don't need to plot the points if you use vectors...you could also use the cosine law from trig