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Find $ a \cdot b $.

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

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03:19

Chris Trentman

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Harvey Mudd College

Baylor University

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.

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If we want to find the dot product between these, I'm first going to rewrite this a little bit. So I'm going to write all the coefficients for these if they're not written and also knows how a We don't have a K term. So that's essentially just saying we have plus Zero K. Um, and now for all the ones that don't have one, remember, it's an implied one in front of it like this. So now remember, if we take the dot product of these two factors, what we want to do is multiply the component part, are these coefficients care and then add everything up. So we're first going to do two times one. So we have two times one and then we're going to add this to when we do one times negative one. So one times, negative one. And then we'll add that to when we multiply zero times one. And if we go ahead and just kind of break this out now, that would give us so two minus one, which is one so a dot be is just going to be one

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