Help with dot product and vectors!!!?

A triangle has its vertices at A(-1,3), B(3,6) and C(-4,4).


a) Show that AB dot AC = -9.


b) Show that, to three significant figures, cosBAC= -0.569

Help with dot product and vectors!!!?
You need to have three dimensional coordinates e.g. (1,3,5) to use the dot product.





In any case...





AB.AC = (a1a2) + (b1b2) + (c1c2)





and





Cosine of angle = AB.AC/ |A| |B|





That is the cosine of the angle = the dot product AB.AC divided by the magnitude of A times the magnitude of B.





Hope this helps.
Reply:a) AB and AC are vectors


AB . AC = (4 3) . ( -3 1) = - 12 + 3 = - 9





b) AB . AC = |AB| |AC|cos A


- 9 = √25 √10 cos A


cos A = - 9 / 5√10


cos A = - 0.569 as required.