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 October 30th, 2011, 08:01 AM #1 Newbie   Joined: Oct 2011 Posts: 2 Thanks: 0 The angle between three vector Hai , I have three point A(X1,Y1,Z1) , B(X2,Y2,Z2) and C(X3,Y3,Z3) How i can get the angle between A to B and A to C ( the angle form by vector AB and AC ) ? This is because most usual problem determine by original axis (that is ,A=(0,0,0) ) Thank You if any one can resolve ! Thank
 October 30th, 2011, 09:38 AM #2 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: The angle between three vector The vector from A(x1,y1,z1) to B(x2, y2, z2) is the same as the vector form (0,0,0) to (x2-x1, y2-y1, z2-z1).
 October 30th, 2011, 10:02 PM #3 Newbie   Joined: Oct 2011 Posts: 2 Thanks: 0 Re: The angle between three vector hai , i get what you have reply ! and another question , the distance and angle between vector AB and AC can be computed using vector BC or not ? for example , distance vector AB and AC = |BC| and again A is not (0,0,0) thank You
 October 31st, 2011, 08:13 AM #4 Math Team   Joined: Sep 2007 Posts: 2,409 Thanks: 6 Re: The angle between three vector If $A= =$ and $B= =$ then the vector from the tip of A to the tip of B is $$. The distance between them is, of course, $\sqrt{(b_1- a_1)^2+ (b_2- a_2)^2+ (b_3- a_3)^2}$. The angle between two vectors is given by their "dot product": $A\cdot B= |A||B|cos(\theta)$ so for $\theta$ the angle between vectors A and B, $cos(\theta)= (a_1b_1+ a_2b_2+ a_3b_3)/[(\sqrt{a_1^2+ a_2^2+ a_3^2})(\sqrt{b_1^2+ b_2^2+ b_3^2})]$.

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angle between 3 vector

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