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I have multiple questions of that kind, the first one was Describe the line from point A(1,2,3) to point B(2,-1,1)

My answer is : V = OA + OB , right ?

Should I do something like V = x1A+x1B , AB = (1+2,2-1,3+1), AB = (3,1,4) ?

Then I have to describe the parallelogram at the origin $$A(1,2,3)$$ made the 2 vectors $$[2,-1,1] and [1,1,1]$$

I ended up with $$X = Ov1 + Ov2 , so X = (1,2,3)[2,-1,1] , (1,2,3)[1,1,1]$$

Then I'll have to describe the form that use four points $$A(1,2,3), B(-1,2,0) C(1,0,1) D(0,1,1)$$

Yeah... I'm confuse.

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up vote 2 down vote accepted

For the first: No, the line from $A$ to $B$ is $\vec V=\vec {OB} - \vec {OA}$. You are essentially moving $A$ to the origin, so need to subtract it.

For the parallelogram: Presumably the corners of the parallelogram are $A, A+v1, A+v2, A+v1+v2$. These are $(1,2,3), (3,1,4)$ and what two others?

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