Angle in between two vectors

What is the angle in radians between the vectors
{a}=(6, -8, 1) and
{b}=(3, -8, -4)?

Use dot product:

a • b = ||a|| ||b|| cosθ
cosθ = a • b / (||a|| ||b||)

a = (6, −8, 1) -------> ||a|| = √(36+64+1) = √101
b = (3, −8, −4) -----> ||b|| = √(9+64+16) = √89
a • b = 18 + 64 − 4 = 78

cosθ = 78 / (√101 √89)
θ = arccos (78/√8989)
θ = 0.604660573 radians (34.64 degrees)

get the dot product by both ways

a.b = (6*3) + (-8*-8) + (1*-4) = 18 + 64 - 4 = 78

a.b = a*b*cos(theta)
= sqrt( 6^2 +(-8)^2 +1^2) * sqrt(9+64+16) * cos (theta)
= sqrt(101*89)*cos( theta )

=>cos (theta)=78/(sqrt(101*89))

=> theta = cos^(-1) (78/94.81)
=> theta = 0.604655424986452 rad

CosB=A.B/|A||B|
|A|=sqrt(6^2+8^2+1)
|A|=sqrt101
|B|=sqrt(3^2+8^2+4^2)
=sqrt89
A.B=78
cosB=[78/sqrt(101*89)]
B=arccos[78/sqrt(101*89)]