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Find $ a \cdot b $.

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

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01:30

Carson Merrill

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

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University of Nottingham

Boston College

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.

02:51

Find $A B$.$$A=\left[\…

00:52

Find $A-B$.$$A=\left[\…

00:17

01:10

Find (a) $4 \mathrm{a}-2 \…

00:55

00:34

Find $5 A+3 B$.$$A=\le…

00:38

in this problem, we are given two vectors A and B, and we're told that we need to multiply our two vectors. We have to find a times B, and that's what we're going to be doing. So eight times we would be equal to our first factor. Five common negative two times or second vector three, comma four. So how would we multiply these vectors? This would be equal to five times three minus two times four. So that simplifies to 15 minus eight. And we find that the product of these two vectors is seven. So I hope that this problem helped you understand a little bit more about how we could multiply two vectors and the process that we go through to find that value.

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