What is the angle between #<-4 , 0 , 7 > # and # < 8 , -5 , 0 > #?

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Answer 1 · 2016-02-12T20:02:15

#114.88^@#

We may use the Euclidean inner product of 2 vectors #A and B# in #RR^n# to find the angle #theta# between them as follows :

#A*B=||A|| ||B|| cos theta#.

So in this case we get :

#theta=cos^(-1)((A*B)/(||A||||B||))#

#=cos^(-1)((-32+0+0)/((sqrt65)(sqrt89)))#

#=114.88^@#.

Note that we could also have used the vector cross product since we work in #R^3# and would of got the same answer.
#AxxB=||A||||B||sintheta#.