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V1 Introduction to vectors

This page Introduces the basic concepts around vectors (which are measurable quantities with direction such as force). It introduces the concept of a scalar (which is a quantity without a direction...

V10 Distance from a point to a plane

The shortest distance from some point in the air down to flat ground, is defined by a line straight down, sitting at right angles to the ground.

V11 Directional derivatives

If you are on the side of a hill, the gradient depends on the direction you look. So the directional derivative is the gradient in a particular direction.

V2 Resolution of vectors

Vector quantities in combination will enhance or counteract each other, depending on their direction. An opposing force for example will lessen another force. However, if the forces (or vector...

V3 Scalar product

What is a scalar product? What is a dot product? This is the result of multiplying the magnitudes of the components of two or more vectors. The result is not a vector, but a scalar (which is...

V4 Vector product

What is a vector product? What is a cross product? The vector product is a vector that is the result of multiplying the magnitudes (size) of two vectors. The magnitude is found using matrices and...

V5 Projection of vectors

In ’Resolution of vectors’ we learned how to resolve vectors in two dimensions along horizontal and vertical axes. It is also possible to resolve one vector along the line of another vector (...

V6 Vector equation of a line

If you want to uniquely define a line, you need to pin it between two points in 3-dimensional space. You can also define a point with a 3-dimensional vector through it. This process uses three types...

V7 Intersecting lines in 3D

Learn how to determine if two lines in three dimensions intersect (cross each other) and, if so, what is their point of intersection?

V8 Equation of a plane

Learn how to find the equation of a plane (a 2-dimensional space): a) through three points or b) given a normal (line at right angles) and a point on the plane or c) given a parallel plane and a...

V9 Intersecting planes

Two 2-dimensional planes will slice through each other (unless they are parallel). Where they slice will be defined by a straight line. There will also be an angle between the two planes.


2 + 2 does not always equal 4 when the problem is translated into a 2 or 3 dimensional space. Vectors are quantities that have both magnitude (size) and direction. This branch of maths is fundamental...