What is the dot product of #<8,-1,4># and #<9,1,5 >#?

1 Answer
Dec 28, 2015

Answer:

#91#

Explanation:

For any 2 vectors #v=(v_1,v_2,....,v_n) and w=(w_1,w_2,...,w_n)# in a real or complex finite dimensional vector space, the Euclidean inner product (dot product) is defined as follows :

#v*w=v_1w_1+v_2w_2+.....+v_nw_n#.

So in this particular case of 3-dimesnional vectors we get

#(8,-1,4)*(9,1,5)=(8xx9)+(-1xx1)+(4xx5)#

#=72-1+20#

#=91#.

(Note that we can also represent the inner product as the angle between the 2 vectors and the norms of the 2 vectors as follows :
#u*v=||u||xx||v||costheta#