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## Vector Resources

Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1] v=?x+?y

Let H be the set of all vector of the form [-4s,-3s,5s]. Find a vector v in R3 such that H=span {v} v=?

Express the vector v= [6,2] as a linear combination of x= [-4,-1] and y[-5,-1]   v=?x+?y

Find the shortest distance from the point P= (7, 6, 4 ) to a point on the line given by l: (x,y,z)= (-7 t, 7 t, 1 t).   the distance is:

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 = <x,y>. Since a position vector... 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,... read more