# Math: Vectors - Collinear

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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.

• Math: Vectors - 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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