Operations involving vectors

There are three kinds of values that appear in vector algebra: scalars, points, and vectors. We can try to add these, subtract them, and multiply them in various ways. Sometimes these operations make sense, and sometimes they don't, with results as in the following table:

	Scalar	Point	Vector	Scalar	Point	Vector	Scalar	Point	Vector
Scalar	Scalar	―	―	Scalar	―	―	Scalar	―	Vector
Point	―	―	Point	―	Vector	Point	―	―	―
Vector	―	Point	Vector	―	―	Vector	Vector	―	Depends

There are various ways to multiply two vectors, with results as in the table below:

Name	Symbol	Result	Order matters?	Depends on lengths?	Depends on right-hand rule?
Dot product	⋅	Scalar	No	Yes	No
Cross product	×	Scalar in 2D, vector in 3D	Yes	Yes	Yes
Tensor product	⊗	Dyad	Yes	No	No

We don't cover the tensor product (or dyads) in this course, but I put it in there just to emphasize that there are more operations on vectors than the ones that we do cover.

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This web page was written in 2014 by Toby Bartels, last edited on 2014 June 12. Toby reserves no legal rights to it.

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