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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, -4, 1 \rangle , b = \langle 0, 2, -2 \rangle $

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$$\cos ^{-1}\left(-\frac{5}{6}\right)=146^{\circ}$$

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Campbell University

Harvey Mudd College

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.

02:43

Find the angle between the…

01:38

04:50

01:25

01:24

01:06

01:31

Find the angle (round to t…

All right, So first, let's find the magnitude today. Ninety two today is one squared plus negative. Four squared plus one squared. That is rad eighteen. Just three, right, too magnitude of B zero squared plus two squared, plus native to squared. You're at a just to read, too. We also want to find the dog product, right. We're going to be using this formula, obviously, eh? B a b o sign. Okay, so the dot product is one time zero last night of two night of four times. Two last one times native to this is negative. Ten. Co signed data. Just a dot Be over, eh? B is the negative ten over three. Rad. Two times to read too. His negative turn over twelve. This is, uh we divide by to hear, Get negative. Not they does equal to co sign in verse. Uh, far native five, six. Okay, so turn that into a calculator. I divided by six negative of that coast on inverse. Yeah, one hundred forty six degrees

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