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Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.)

$ a = \langle -1, 3, 4 \rangle , b = \langle 5, 2, 1 \rangle $

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Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Campbell University

Baylor 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 angle between the…

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lesson lesson. We'll finally younger between two vectors A and B. So do this by finding the dot product, and that has given us the magnitude of vector eight times the magnitude of vector B cause Sita, where zika is the angle between two vectors. So here we'll make that cost fee to the subject of the equation So we can divide both sides by the magnitude of the vectors, so that this will cross out that then we have the costs of the angle as a dot be all over the magnitude of a the magnitude of the Okay. So here the cost theater is equal to Yeah, the doctor border took the back test 5 to 1, then the magnitude of them. Uh huh. Oh, so in the dot product, you would multiply the correspondent cams, then you some them some of the correspondent times. Oh, Okay, so here we have one plus nine plus 16. Okay, so that keeps us 26 then. Here we have 25 plus four plus one. That gives us 30. Okay, so the course of the angle, it's negative. Five last six plus five, all of us, the square root of All right. 780. That is 30 times 26. Okay, so we have the cost feature of that is four. So five negative five. Last six gives us one plus four. That gives us what's going on. That gives us five. Oh, so five over square root of 780 Okay, so to get a theater, we take that course or five on the square root of That's Okay. So the articles of 0.1 79 0 to 9, and that is 79 0.686 793 08 to 1 degrees. And this is opposed. Made leaf 80 degrees. Okay, so the angle between the vector A and Vector B supposedly eat the grease. Okay. Thanks for time at the end of the lesson.

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