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Vectors, Pure and Applied by T. W. Körner

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2

A little geometry

2.1 Geometric vectors

In the previous chapter we introduced column vectors and showed how they could be used to study simultaneous linear equations in many unknowns. In this chapter we show how they can be used to study some aspects of geometry.

There is an initial trivial, but potentially confusing, problem. Different branches of mathematics develop differently and evolve their own notation. This creates difficulties when we try to unify them. When studying simultaneous equations it is natural to use column vectors (so that a vector is an n × 1 matrix), but centuries of tradition, not to mention ease of printing, mean that in elementary geometry we tend to use row vectors (so that a vector is a 1 × n matrix). Since one ...

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