If $A = < - 6, 2, 5 >$ $A = <-6 ,2 ,5 >$ , $B = < - 8, 3, 4 >$ $B = <-8 ,3 ,4 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

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If $A = < - 6, 2, 5 >$ $A = <-6 ,2 ,5 >$ , $B = < - 8, 3, 4 >$ $B = <-8 ,3 ,4 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

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Answer 1 · 2016-03-06T13:40:25

$α ≅ 63^{o}$ $alpha~=63^o$

Explanation:

$C = (- 6 - (- 8)), (2 - 3), (5 - 4)$ $C=(-6-(-8)),(2-3),(5-4)$
$C = < 2, - 1, 1 >$ $C=<2,-1,1>$
$A \cdot C = A_{x} \cdot B_{x} + A_{y} \cdot B_{y} + A_{z} \cdot B_{z}$ $A*C=A_x*B_x+A_y*B_y+A_z*B_z$
$A \cdot C = - 12 - 2 + 5 = - 9$ $A*C=-12-2+5=-9$
$| | A | | = \sqrt{36 + 4 + 25} | | A | | = \sqrt{65}$ $||A||=sqrt(36+4+25)" "||A||=sqrt65$
$| | C | | = \sqrt{4 + 1 + 1} | | C | | = \sqrt{6}$ $||C||=sqrt(4+1+1)" "||C||=sqrt6$
$A . C = | | A | | \cdot | | C | | \cdot cos α$ $A.C=||A||*||C||*cos alpha$
$- 9 = \sqrt{65} \cdot \sqrt{6} \cdot cos α =$ $-9=sqrt65*sqrt6*cos alpha=$
$- 9 = \sqrt{65 \cdot 6} \cdot cos α$ $-9=sqrt(65*6)*cos alpha$
$- 9 = \sqrt{390} \cdot cos α$ $-9=sqrt390*cos alpha$
$- 9 = 19, 74 \cdot cos α$ $-9=19,74*cos alpha$
$cos α = - \frac{9}{19, 74}$ $cos alpha=-9/(19,74)$
$cos α = 0, 445927051672$ $cos alpha=0,445927051672$
$α ≅ 63^{o}$ $alpha~=63^o$

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If $A = < - 6, 2, 5 >$ $A = <-6 ,2 ,5 >$ , $B = < - 8, 3, 4 >$ $B = <-8 ,3 ,4 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?

1 Answer

Explanation:

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If A=<−6,2,5>A = <-6 ,2 ,5 >, B=<−8,3,4>B = <-8 ,3 ,4 > and C=A−BC=A-B, what is the angle between A and C?

1 Answer

Explanation:

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If $A = < - 6, 2, 5 >$ $A = <-6 ,2 ,5 >$ , $B = < - 8, 3, 4 >$ $B = <-8 ,3 ,4 >$ and $C = A - B$ $C=A-B$ , what is the angle between A and C?