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

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Answer 1 · 2016-02-12T20:02:15

${114.88}^{\circ}$ $114.88^@$

We may use the Euclidean inner product of 2 vectors $A and B$ $A and B$ 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.
$AxxB=||A||||B||sintheta$ .

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