If $A = < 5, 4, 8 >$ $A = <5 ,4 ,8 >$ , $B = < 2, - 7, 6 >$ $B = <2 ,-7 ,6 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

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Answer 1 · 2018-06-18T22:00:10

$θ = arccos \frac{75}{\sqrt{14070}}$ $theta = arccos frac{75}{sqrt 14070}$

$C = ((3), (11), (2)), A = ((5), (4), (8))$

$A * C = |A| * |C| * cos theta$

$cos theta = frac{15+44+16}{sqrt{25+16+64} sqrt{9+121+4}}$

$cos theta = frac{75}{sqrt{3*5*7*2*67}}$

If A = <5 ,4 ,8 >A=<5,4,8>A = <5 ,4 ,8 >, B = <2 ,-7 ,6 >B=<2,−7,6>B = <2 ,-7 ,6 > and C=A-BC=A−BC=A-B, what is the angle between A and C?