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Vector Calculus Resources


Vector Functions

Vector Functions We will use the cross product and dot product of vectors to explore equations of lines and planes in 3 dimensional space. Vector functions have an input t and an output of a vector function of t. Position Vectors A position vector is a vector whose initial point is fixed at the origin so that each point corresponds to P = <x,y>. Since a position vector... read more


Properties of Vectors

Properties of Vectors Vectors follow most of the same arithemetic rules as scalar numbers. The following are various properties that apply to vectors in two dimensional and three dimensional space and are important to keep in mind Addition of Vectors Scalar and Vector Properties Dot Product Properties The Dot Product is defined as as... read more


Introduction to Vectors

Vectors Vectors are usually used to represent velocity and acceleration, force, and other directional quantities in physics. Vectors are quantities with size and direction. The objects that we have worked with in single variable calculus (Calculus 1 and 2) have all had a quantity, i.e. we were able to measure them. Some quantities only have size, such as time, temperature,... read more


Multivariable and Vector Calculus

Multivariable Calculus In calculus, we have dealt with functions of x in two dimensional space. Multivariable Calculus, also known as Vector Calculus, deals with functions of two variables in 3 dimensional space, as well as computing with vectors instead of lines. In single variable calculus, we see that y is a function of x In multivariable calculus, z is a function... read more