If $A = <2 ,4 ,-7 >$ , $B = <3 ,8 ,2 >$ and $C=A-B$ , what is the angle between A and C?

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Answer 1 · 2016-05-13T15:21:21

56.78 degrees

C = A-B = < (2-3), (4-8), (-7-2)> = <-1,-4,-9>

||A||= $sqrt (2^2 +4^2+(-7)^2$ = $sqrt69$

||C||= $sqrt((-1)^2 +(-4)^2 +(-9)^2)$ = $sqrt98$

A.C= 2(-1) +4(-4) + (-7)(-9)= 45

If $theta$ is the angle between A and C,

$costheta = 45/(sqrt69 sqrt98)$ =0.5479

$theta$ =56.78 degrees

If A = <2 ,4 ,-7 >A = <2 ,4 ,-7 >, B = <3 ,8 ,2 >B = <3 ,8 ,2 > and C=A-BC=A-B, what is the angle between A and C?