# The Application of Vectors

This word document gives methods to work out angles, intersections and distances between lines, planes and points. Diagrams are included in each case.

- Created by: William Matcham 1992
- Created on: 21-05-11 21:50

First 278 words of the document:

1

The Application of Vectors

Items Angle between Distance between Intersection of

Plane and plane 1. 2. 3.

Plane and line 4. 5. 6.

Plane and point 7. 8. 9.

Line and point 10. 11. 12.

Line and line 13. 14. 15.

Point and point 16. 17. 18.

The basics of vectors

A vector is a quantity with both a magnitude and a direction. A scalar is a quantity with just

magnitude.

If I say that I am running at 10ms-1 , this only gives a sense of only how fast I am running i.e. a

scalar. However if I say that I am running at 10ms-1 due north, then it gives a sense of

magnitude and direction i.e. a vector quantity.

To-scale vectors are drawn as arrows, with their length representing magnitude of the

vector quantity and their direction representing the vector's direction.

Vectors are denoted as letters with lines or squiggles above. In textbooks, they are

emboldened.

For some vector a

~ , |~

a| or a denotes the magnitude of the vector.

A vector with a hat denotes a unit vector, which is the respective vector that has unit

magnitude. Hence the unit vector of a

~ is written a

^ (read as `a hat'). a a

~.

^ =a

Vectors can be considered on the 3D Cartesian plane, and can be expressed as the sum of

^, ^

multiples of the unit vectors i ^ , which are parallel to the x , y and z axis respectively.

j and k

The addition and subtraction of vectors is simple: the respective components of vectors are

added or subtracted.

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