- #1
Macleef
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Homework Statement
Using vectors, demonstrate that these points are collinear.
a) P(15 , 10) , Q(6 , 4) , R(-12 , -8)
b) D(33, -5, 20) , E(6, 4, -16) , F(9, 3, -12)
Homework Equations
[tex]\frac{x_{1}}{x_{2}}[/tex] = [tex]\frac{y_{1}}{y_{2}}[/tex]
[tex]\frac{x_{1}}{x_{2}}[/tex] = [tex]\frac{y_{1}}{y_{2}}[/tex] = [tex]\frac{z_{1}}{z_{2}}[/tex]
The Attempt at a Solution
a)
Vector PQ = (-9 , -6)
Vector QR = (-18 , -12)
Vector RP = (27 , -18)
(-9 / 27 / -18) = (-6 / -18 / -12)
Therefore, not collinear.
b)
Vector DE = (-27, 9, -36)
Vector EF = (3, -1, 4)
Vector FD = (24, -8, 32)
(-27 / 3 / 24) = (9 / - 1 / -8) = (-36 / 4 / 32)
Am I correct or did I do something wrong? If I did, can you please point it out and tell me on how to fix it?
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