We calculate eigenvalues of a 3 by 3 matrix.

This screencast shows the general method, together with an example, of finding the equation of a straight line in 3D in vector form, scalar parametric form and Cartesian form

This recording explains the relationship between Polar and Cartesian coordinates of a 2D curve. An example is then given of converting a polar equation into Cartesian form and an example is given of converting a Cartesian equation into polar form.

Example of using the multivariate chain rule where z=f(x,y) and x and y are both functions of t.

Considering a line written in scalar parametric form and a plane written in form ax + by + cz = d, three examples investigate if and where line and plane intersect: in one point; the line lies on the plane; or line and plane are parallel and never meet

This recording starts by showing how the equation of a plane relates to its normal vector. An example is then done to show how this allows us to find the equation of a plane, provided we also know a point on the plane.

Given a point and a line on a plane, we find the equation of the plane.A second point on the plane is identified, and hence a vector on the plane. A normal vector to the plane is calculated using the vector product.The equation of the plane is then found.

An example of how to find the curvature and the radius curvature at a particular point of a curve where the equation of the curve has form y = f(x)

This screencast gives two examples of converting the parametric equations of 2D curves into Cartesian equations, and includes a discussion on the importance of considering any restrictions of the domain of the resulting Cartesian equations in each case.

This recording starts by giving the general formula for calculating the angle between two planes by finding the angle between their normal vectors. An example is then given to illustrate this.