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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 (3, -1), B (2, 3) $

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$$<-1,4>$$

00:29

Alan Ghazarians

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 2

Vectors

Johns Hopkins University

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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.

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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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Find a vector a with repre…

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Find vector with represent…

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Find a vector with represe…

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we are given a directed line segment A B and rest to find a victor with the representation of this line segment were asked to draw the victor for the line segment A B and the equivalent representation starting at the origin. So we're told that point A is three negative one, and point B is at 23 Yeah, to find a vector with the representation given by this line segment, we want the vector to have components, which are the difference between the components of A and B, and it has two point in the same direction as line segment 80. So we take the X component of B two and subtract the X component of a three. Then we take the Y component of the three. Some track to the wagon point of a negative one, and we get the vector with components negative one four. So this is the vector, which we call Vector A. So now I'll draw both directed line segment AB and the equivalent representation. Let's see, I'm going to need extra range from 0 to 3 and wide range from negative 1 to 4. So they directed line segment. This has the points A which is three negative one located here and B, which is 23 We draw a ray starting at a towards B. So it looks something like this. I should let x range from negative one as well. My mistake, then the equivalent vector at the origin. Well, the initial point is going to be the origin and the terminal point of this vector is negative. 14 located about here and so are equivalent vector A looks something like this. Notice. These two vectors are parallel pointing in the same direction and have equivalent magnitudes.

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