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

1 Answer
Trevor Ryan.
Dec 28, 2015

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

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