When it comes to analytic geometry, I am little confused about the use of vectors. For example, throughout high school, one works in ##\mathbb{R}^2##, and geometric objects such as lines are described using equations relating two variables, the x and y coordinate, such as y = 2x + 1. However, when we move to three-dimensions, it seems that vectors as well as relations between coordinates are used. For example, to represent a line with vectors, we might use something like ##\vec{r} = \vec{r}_0 + t \vec{v}##, while we can also represent the same line with the simultaneous equation such as ##x = 2y + 1,~ y = 3z - 5##, just as a random example. And for planes , we just use ##ax+by+cz+d=0##. This leaves me wondering why we use vectors at all. It seems like vectors are another a way just to represent a triple of coordinates. If this is the case, why don't we just use equations relating variables all the time?(adsbygoogle = window.adsbygoogle || []).push({});

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# I DIfference between vectors and relations of points

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