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

$ a = 4i - 3j + k , b = 2i - k $

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$52^{\circ}$

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

University of Nottingham

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.

03:35

Find the angle between the…

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02:18

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01:25

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01:53

Compute the angle between …

02:43

01:00

Find (a) the dot product o…

01:49

01:24

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01:18

Okay, so we're gonna use this formula to figure out what this angle is. So first we need a dot Be, that's going to be four times two plus negative. Three times zero plus one times one. Um so it's gonna end up being nine. Now, we need the magnitude of a or squared plus negative three squared plus one squared. And this ends up being right. 26. Then we got the magnitude of B got two squared, plus zero squared, plus negative one squared square to five. So then just manipulating this formula a little bit, we end up with this. And then we got nine over rad. Five times read 26. So co sign inverse of this whole thing will be equal to data.

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