Vectors Written by tutor Megan C. When working with equations and mathematical operations with scalar quantities, you are looking at only the magnitude of the numbers. Therefore, when you solve a problem and find a numerical answer, you have the size of the answer but not its position. Using vectors instead of simple numbers can help you solve problems where you need more information... read more
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 = . Since a position vector cannot be translated, it is... read more
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
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, or weight. These quantities... read more
Let f(x, y, z)=yz+xz-6. At the point x=1, y=1, z=1, find the unit vector that points in the direction for which f is increasing at the fastest rate.
Let F(x, y) be the vector field ((x-y)/(x^2+y^2), (x+y)/(x^2+y^2)). Compute curl(F).
Find a potential function for the vector field f(x, y)=2x/y i+(1-x^2)/y^2 j.
Find the principal unit normal vector to the curve defined by r(t)=<t, t^2>. T(t)=1/sqrt(1+4t^2)i+2t/sqrt(1+4t^2)j I need to find T'(t) using quotient rule but don't know...