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Describe in words the region of $\mathbb{R}^{3}$ represented by the equation(s) or inequalities.$x^{2}+y^{2}=4, \quad z=-1$

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 1

Three-Dimensional Coordinate Systems

Vectors

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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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Describe in words the regi…

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Okay, here we're in 3 d space, but if we take the first part of the item here in 2 d space, what we have is a circle and there's x here is y- is a circle of radius. 4 point sorry: radius. 2 center, the origin, it's of the form x, squared plus y squared, equals r squared circle, central 00 radius, r n. Now the z axis will be here coming out of the board straight toward you point. So all i do, then, is get the circle and move it off the page, if you like, towards the plane, z, equals negative 1 point, lets kind and draw it here here is x y here is z and the circle will be like that, and here is Negative 1 on the z axis, so it's the same circle you see on the left pulled out of the page if you like, and the center is like going to be 00 negative 1.00 for x and y and negative 1 for z, and we want here is The region described okay, so it's going to be all points of the circle x, squared plus y squared equals 4, the radius 2. In other words, it lies on the plane. Z equals negative 1 t's. It.

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