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A : (2, 1, -1)
B : (3, 4, 5)
C : (-1, 2, 3)
Ditanya :
cosinus sudut antara AB dan AC
jawab :
AB = B - A
= (3, 4, 5) - (2, 1, -1)
= (1, 3, 6)
AC = C - A
= (-1, 2, 3) - (2, 1, -1)
= (-3, 1, 4)
AB.AC = (1, 3, 6).(-3, 1, 4)
= (-3+3+24)
=24
|AB| = akar 1^2 + 3^2 + 6^2
= akar 46
|AC| = akar (-3)^2 + 1^2 + 4^2
= akar 26
|AB|.|AC| = akar 46 × akar 26
= 2 akar 299
cosinus = AB.AC / |AB|.|AC|
= 24/2akar299
= 24 × 2 akar 299 / 4 × 299
= 12 akar 299 / 299
.
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aduh bener ngga ya? :3
maaf kan saya kak milieth