If $A = < 4, 7, 2 >$ $A = <4 ,7 ,2 >$ , $B = < 7, 1, - 4 >$ $B = <7 ,1 ,-4 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

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Answer 1 · 2016-07-18T09:14:34

Given

$A = < 4, 7.2 > and B = < 7, 1, - 4 >$ $A=<4,7.2> and B=<7,1,-4>$

$:.C=A-B=<-3,6,6>$

If the angle betwee A and C be $theta$ then

$costheta=(A.C)/(abs(A)abs(B))$

$=(<4,7,2>.<-3,6.6>)/(sqrt(4^2+7^2+2^2)sqrt(3^2+6^2+6^2)$

$=(-12+42+12)/(sqrt69sqrt81)$

$=42/((sqrt69).9)=14/(3sqrt69)$

$=cos^-1(14/(3sqrt69))=55.81^@$

If A = <4 ,7 ,2 >A=<4,7,2>A = <4 ,7 ,2 >, B = <7 ,1 ,-4 >B=<7,1,−4>B = <7 ,1 ,-4 > and C=A-BC=A−BC=A-B, what is the angle between A and C?