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# Another p3 vectors question watch

1. the points A, B and C have position vectors, 2i + j + k, 5I + 7j + 4k, and i - j respectively.

Prove A,B and C lie on a straight line
2. (Original post by sequence123)
the points A, B and C have position vectors, 2i + j + k, 5i + 7j + 4k, and i - j respectively.

Prove A,B and C lie on a straight line
AB = (3,6,3)
BC = (-4,-8,-4)

These are multiples of one another and so AB and BC are in the same direction and ABC lie on a line
3. AH i see, are there any other methods for showing thay all lie on the same line?
4. (Original post by sequence123)
AH i see, are there any other methods for showing thay all lie on the same line?
yes but I guess that's the quickest one.

You could try writing down the general cartesian form of an equation in 3D and show that the three points make consistent constraints on the coefficicents but that'd be rather laborious

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