- #1

Macleef

- 30

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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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