Math 252 Lecture 04: Monday, January 11th 1999.

We continued discussing the equations for a plane in space [Transparancy 1]. In vector form, the equation of a plane is simply the dot-product of the normal vector with any vector in the plane. By expressing the vectors in terms of their components, one gets an equation of the form ax + by + cz = d , where the coefficients of x, y, and z are the components of the normal vector.

The orientation of a plane in space was considered [Transparancies 1 and 2]. The right-hand rule was defined.

The concept of a vector product (also known as a "cross product") was defined [Transparancy 2]. Justification for this definition was given in terms of torque and magnetic force.

By exploring the cross-product of the unit vectors of a right-handed coordinate system, we came up with a rule for the components of a general cross-product [Transparancy 3]. (We had to assume the distributivity of the cross product here. It will be proven next lecture.) The components of a cross product can be expressed in terms of the determinant of a matrix. This is a useful device for calculating cross-products.

A geometrical interpretation of the cross product in terms of the area of a parallelogram was given [Transparancy 4].

Here are the scanned-in transparancies, in full-colour JPEG format:


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Revised January 1999 by John Hebron.