What is the angle between #<2,5,4 ># and #< 6,8,1 >#?

1 Answer
Dec 27, 2015

#33.83^@#

Explanation:

There are 2 methods we can use to calculate this algebraically, either using the vector cross product or the vector inner product.
I shall use the latter method as it is quicker and also more general.

The angle between any 2 vectors #A and B# in any dimensional vector space may be given by the inverse cosine of the Euclidean inner product of the 2 vectors divided by the product of the norms of the 2 vectors.
ie. #costheta=(A*B)/(||A||*||B||)#

#therefore theta=cos^(-1) (([(2,5,4) * (6,8,1)]) / (||((2,5,4))|| * ||((6,8,1))||))#

#=cos^(-1)((12+40+4)/(sqrt(45sqrt101)))#

#=33.83^@#.