Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1]. v=?x+?y
Express the vector v=[6,2] as a linear combination of x=[-4,-1] and y=[-5,-1]. v=?x+?y
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
You are looking down at a map. A vector U with |U| 1 points north and a vector V with |V|= 9 points northeast. The crossproduct UxV points: A) south? B) northwest? C) up? D) down...
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:
Find a unit vector with positive first coordinate that is orthogonal to the plane through the points P = (-5, -5, -4), Q = (-1, -1, 0), and R = (-1, -1, 5).
Find an equation of the plane through the point (-3, -1, -2) and parallel to the plane 3x + 2y - 5z = -4. Do this problem in the standard way
Find an equation of the plane through the point (-5, -1, 1) and perpendicular to the vector (-1, 1, 5). Do this problem in the standard way
If DEF are midpoints of triangle ABC PROVE OA+ OB+ OC =OD +OE +OF
Let x = [-4, 4,5] and y=[0,0,-3] Find the dot product of x and y x.y=?
Let u=(1,-1,0) and v=(1,-2,-3). Find the vector w=2u-3v and its additive inverse. w= -w=
Find the angle between the vectors [1 4 -5] and [5 -5 4]
Determine the angle between vector PQ and the positive x-axis, given endpoints P(4,7) and Q (8,3)
Determine the interior angles of triangle ABC for A(5,1), B(4, -7), and C (-1,-8)
A force, F of 25 N is acting in the direction of a = (6,1). a) Find a unit vector in the direction of a. b) Find the Cartesian vector representing the force, f, using your...
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