Calculating Angles between Vectors: Step-by-Step Guide

[pokerfan91]

ive got the formula down as angle=cos^-1[(u.v)/(||U||||v||)

with my u as 3,1,2 and v as -2,3,4 this gives me cos^-1[(-6i+3j+8k)/root406) where do i go from here?

 

[Defennder]

What is dot product supposed to give you? What did you get instead?

 

[pokerfan91]

that is what the dot product is ment to give me isn't it i just have no idea where to go after that to get the angle

 

[nicksauce]

No it isn't. The dot product is supposed to give you a scalar (ie a number), but you wrote that it gives you a vector. You can't very well take the arccosine of a vector can you?

 

[HallsofIvy]

$$a\vec{i}+ b\vec{j}+ c\vec{k}\cdot d\vec{i}+ e\vec{j}+ f\vec{k}$$
is defined as
$$ad+ be+ cf$$
a number, NOT as
$$ad\vec{i}+ be\vec{j}+ cf\vec{k}$$