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I am looking for resolution for a constant problem at work. When writing algebra questions I will say something like "Find a Cartesian equation of the plane passing through the points (1,2,3), (4,5,6) and (7,8,9)." But the applied mathematicians on the exam committee ALWAYS want to change it to "Find a Cartesian equation of the plane passing through the points with position vectors (1,2,3), (4,5,6) and (7,8,9)." WHY? I don't see the problem?? They are constantly agonising over points vs position vectors of points. What's the point? Or is it What's the vector? Do not get it. Why burden both yourself and the students with this distinction? Surely a plane is a collection of points not position vectors of points. ??

Mathman
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  • Loosely speaking the question you were given is on $\mathbb{R}^3$ which is coincidentally a vector space. Hence "point" and 'vector" is almost interchangable. – IAmNoOne Apr 23 '20 at 07:57

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$\mathbb{R}^n$ is a vector space and therefore also an affine space that is all vector can be see as point . what is the difference between a vector and a point ?

What is the difference between a point and a vector?