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What does the equation $ x = 4 $ represent in $ \mathbb{R}^2 $? What does it represent in $ \mathbb{R}^3 $? Illustrate with sketches.

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A line parallel to the $y$ -axis and 4 units to the right of it; a vertical plane parallel to the $y$ -plane and 4 units in front of it.

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

Johns Hopkins University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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.

00:37

If $2^{x}=3,$ what does $4…

00:53

00:49

Explain why $x^{2}=4$ is e…

02:39

If $4^{x}-4^{x-1}=24,$ wha…

02:53

Solve for $x.$$$4^{x+2…

here. Let us two figures. So first we are too since our police airplane. So at this fort is just lying or two we can see here. This is for zero. And it is just This is just the graph ofthe ethics Courtyard, too. And because there are three other is like, Ah, three dimension of space and we fix one coordinates, they are to control them freely. So it's gonna be like playing and plain on the point four zero zero lies in the plane. And playing has a no matter its way C in the normal actor is going to be parent out to X success. And the plane, the whole place is gonna be parallel to the y. Oh, ze pain. So that is what we want.

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