Loading module…
What you will learn in Vectors
1. Scalars, Vectors and Representation
Some quantities need a direction to be meaningful, and a vector is the object that carries one.
2. Components and Resolution
Splitting a vector into two perpendicular pieces — and the axis choice that decides which two.
3. Vector Addition and Subtraction
The triangle law and the parallelogram law are one construction, and magnitudes do not add.
4. Unit Vectors and Direction
Dividing by your own magnitude keeps the direction and discards the size.
5. The Dot Product
How much of one vector points along another — as a projection, as an angle test, and as an exact zero when they are perpendicular.
6. Vectors in Physics
The same operations in three physical situations, with the boundary between the two subjects stated — and the readiness check Physics's gate points at.
7. The Cross Product
A product whose answer is a vector — its length an area, its direction a normal, and its order mattering.
8. The Scalar Triple Product
The volume of the box three vectors make — and zero exactly when they lie in a plane.
9. Three-Dimensional Coordinates
A third axis, eight octants, and every two-dimensional formula gaining one more term.
10. Direction Cosines and Direction Ratios
The three angles a direction makes with the axes, and the identity their cosines satisfy.
11. Lines in Space
A point and a direction — and the Cartesian form that cannot describe some perfectly ordinary lines.
12. Planes in Space
A plane is a direction it is perpendicular to, plus how far along that direction it sits.
13. Angles Between Lines and Planes
Three kinds of angle, and one of them is the complement of what you naturally compute.
14. Shortest Distances and Skew Lines
Two lines that never meet and are not parallel — which cannot happen on a page.