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The position vector of A,B,C are (hati+2...

The position vector of A,B,C are `(hati+2hatj+3hatk),(-2hati+3hatj+5hatj)` and (`7hati-hatk`) respectively. Prove that A,B and C are collinear.

Text Solution

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`vec(AB)`=position vector of B-position vector of A.
`=-3hati+hatj+2hatk`
And `vec(BC)`=position vector of C-position vector of B
`=9hati-3hatj-6hatk`
Clearly `vec(BC)=-3vec(AB)`
This shows that the vector `vec(BC)` and `vec(AB)` are collinear. Hence points A,B and C are collinear.
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