Math: Vectors  Collinear
posted by Anonymous .
Can you please check whether my answers are correct? If they aren't, how would you find if the points are parallel to one another with 3 coordinates?
Using vectors, demonstrate that these points are collinear.
a)
P(15 , 10)
Q(6 , 4)
R(12 , 8)
Vector PQ = (9 , 6)
Vector QR = (18 , 12)
Vector RP = (27 , 18)
(9 / 27 / 18) = (6 / 18 / 12)
Therefore, not collinear.
b)
D(33, 5, 20)
E(6, 4, 16)
F(9, 3, 12)
Vector DE = (27, 9, 36)
Vector EF = (3, 1, 4)
Vector FD = (24, 8, 7)
(27 / 3 / 24) = (9 /  1 / 8) = (36 / 4 / 7)
Therefore, not collinear.

no
Vector PQ = (9 , 6)
Vector QR = (18 , 12)
so vector QR = 2(9,6) = 2PQ
so P,Q and R are collinear since we were able to express them as a linear combination.
same thing in b)
notice that (27,9,36) = 9(3,1,4) 
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