-
Many concepts in physics may be represented by vectors. A vector has both a size (called its magnitude) and a direction. This module explains how vectors may be added together. Scalars and Vectors Many physical quantities can be classified into one of two groups: scalars or vectors. Scalar quantities are...
-
Introducing the basic concept of vectors (which are measurable quantities with direction such as force) and the concept of a scalar (which is a quantity without a direction such as heat or thermal energy). We cover vector components (aligned along the horizontal and vertical or the 3-dimensional axes), unit vectors...
-
The shortest distance from any point in the air to the ground is defined by a line sitting at right angles to the ground going straight down. Learn how to find the perpendicular (right angle) distance from a point to a plane. What do we mean when we talk about...
-
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. (See also Linear graphs) Learn how to find the directional derivative of a function of two variables f(x,y) or three variables g(x,y,z)...
-
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 quantities) do not act along exactly the same line, it is difficult to know how they will interact. This task is...
-
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 without direction). There are two ways to multiply two vectors: The scalar or...
-
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 determinants). The result of the cross product is another vector, and the direction is perpendicular...
-
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 (instead of along the x-y axes). (See also Linear graphs) Learn how to find the projection (resolution) of...
-
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 of equations. Learn how to find the vector equation, the parametric equation, and the...
-
Learn how to determine if two lines in three dimensions intersect (cross each other) and, if so, what their point of intersection is. (See also Linear graphs) In order to find the point of intersection of two lines in three dimensional space, it is best to have both equations in...
-
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 point on the plane. (See also Linear graphs) A plane is...
-
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. Learn how to determine the angle between two intersecting planes and the equation of the line of intersection....
-
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 to physics and engineering to represent physical quantities that have a direction. The University...
