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Find the angle between a diagonal of a cube and a diagonal of one of its faces.
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Calculus 3
Chapter 12
Vectors and the Geometry of Space
Section 3
The Dot Product
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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The problem is find the angle between a diagonal of a cube and a diagonal of 1 of its faces. Look at this graph here. So this is the x y d i x y axis and the axis. So this factor is the diagonal this cube here. We assume the last of its edges is equal to 1 point, so the vector of the diagonal of this cube is equal to the use. V is equal to 11 and 1, and a delganal of 1 is basis. This factor this is equal to 10 and 1. Here we denote the angle between these 2 is so we have cosine. Theta is equal to u dot v over magnitude of u times magnitude of v. This is equal to 2 over root of 2 times 3, so this is equal to 2 over root iv. 6 point: this is equal to root of 6 over 3 point, so theta is equal to cosine niverse root to 6 over.
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