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Find the sum of the given vectors and illustrate geometrically.
$ \langle 3, 0, 1 \rangle , \langle 0, 8, 0 \rangle $
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00:40
Alan Ghazarians
Calculus 3
Chapter 12
Vectors and the Geometry of Space
Section 2
Vectors
Johns Hopkins University
Missouri State University
University of Michigan - Ann Arbor
Idaho State University
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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Find the sum of the given …
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let's illustrate the some of this factor geometrically, we're going to do so by getting rid of the X and Y axis as well as the grid. So we're going to have our X, Y Z coordinate system here And we see that we have the vector 301. That's going to be three 0 1. So like right about here And then we're gonna have 080. So it's gonna be along here, I'm gonna say that that's right here. So we're gonna have our factor that looks like this, we want to add them together now. So when we do that a little more complicated in three dimensions, but we see that it's going to end up being with the parallelogram rule. Eventually it looks something like this. I'm gonna it's gonna match up with the parallelogram right here. So maybe we should draw it a little bit more like this, that's probably better. So disregard this one right here, So this is our new vector and the sum is going to be 381. That's the final factor.
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