How Do You Calculate the Angle Between Two Vectors?

[Danatron]

Hi Guys,

Im working on finding an angle between two vectors.

a [ 1,2,3 ]
b [ 4, -1, 0]

//a// = sqrt(1^2+2^2+3^2) = sqrt14
//b// = sqrt(4^2+(-1)^2+0^2 = sqrt17

Dot product
1.4 + 2.-1 + 3.0 = 2

cos^-1 2/ sqrt14 sqrt17
cos^-1 (1/( ? )


Thanks

 

[ehild]

Hi Guys,

Im working on finding an angle between two vectors.

a [ 1,2,3 ]
b [ 4, -1, 0]

//a// = sqrt(1^2+2^2+3^2) = sqrt14
//b// = sqrt(4^2+(-1)^2+0^2 = sqrt17

Dot product
1.4 + 2.-1 + 3.0 = 2

cos^-1 2/ sqrt14 sqrt17
cos^-1 (1/( ? ) Thanks

What is the problem? The cosine of the angle is $\frac{2}{\sqrt{17}\sqrt{14}}$. Just type into your calculator, and take 'inverse cosine' of the result.

And next time write out the parentheses. cos^-1 2/ sqrt14 sqrt17 means cos^-1(2) * sqrt(14) *sqrt(17) which has no sense.

ehild