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Find a vector a with representation given by the directed line segment $ \vec{AB} $. Draw $ \vec{AB} $ and the equivalent representation starting at the origin.
$ A (0, 6, -1), B (3, 4, 4) $
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01:47
Wen Zheng
Calculus 3
Chapter 12
Vectors and the Geometry of Space
Section 2
Vectors
Missouri State University
Campbell University
Baylor University
University of Nottingham
Lectures
02:56
In mathematics, a vector (from the Latin word "vehere" meaning "to carry") is a geometric entity that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. Vectors play an important role in physics, engineering, and mathematics.
11:08
In mathematics, a vector (from the Latin word "vehere" which means "to carry") is a geometric object that has a magnitude (or length) and direction. A vector can be thought of as an arrow in Euclidean space, drawn from the origin of the space to a point, and denoted by a letter. The magnitude of the vector is the distance from the origin to the point, and the direction is the angle between the direction of the vector and the axis, measured counterclockwise.
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our goal for this problem is to um Draw the vector. So knowing are two points. Um We can I recognize that we're no longer dealing with two dimensional graphs and said we're going to be dealing with three dimensional graphs. So we'll get rid of the grid as well as the Y axis and X axis. So by getting rid of this, we can now draw our new coordinate system. This will be the X, Y Z coordinate system. So we have that are points are going to be 06 -1. So this is the X direction we go zero, This is the white direction we go six. Um And then down one. So let's say this is six, This is -1. So we see it's down here, so that's point A. And then point B is 344 So it's going to be right about here, four and then appears about four. So I have a point somewhere right about here, and then we'll see that this vector here can be translated over to the origin.
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