CB = b - c
= (10-5, 9-3, -6-2)
= (5, 6, -8)
|CB| = √(5^2 + 6^2 + (-8)^2)
= √(25 + 36 + 64)
= √125 = 5√5
CA = a - c
= (4-5, 1-3, 2-2)
= (-1, -2, 0)
|CA| = √((-1)^2 + (-2)^2 + 0)
= √(1 + 4 + 0) = √5
Cos C = (CB.CA)/(|CB|.|CA|)
= (5(-1) + 6(-2) + (-8)(0))/(5√5 . √5)
= (-5 - 12 + 0)/25
= -17/25 (b)
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CB = b - c
= (10-5, 9-3, -6-2)
= (5, 6, -8)
|CB| = √(5^2 + 6^2 + (-8)^2)
= √(25 + 36 + 64)
= √125 = 5√5
CA = a - c
= (4-5, 1-3, 2-2)
= (-1, -2, 0)
|CA| = √((-1)^2 + (-2)^2 + 0)
= √(1 + 4 + 0) = √5
Cos C = (CB.CA)/(|CB|.|CA|)
= (5(-1) + 6(-2) + (-8)(0))/(5√5 . √5)
= (-5 - 12 + 0)/25
= -17/25 (b)