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Find $ a \cdot b $.

$ \mid a \mid = 80 $ , $ \mid b \mid = 50 $ , the angle between $ a $ and $ b $ is $ \frac{3 \pi}{4} $

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01:33

Chris Trentman

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Campbell University

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

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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01:57

So this case for us to find the dot product, the form what are going to want to use is the one that I have on the board where it is going to be the dot product of A and B is the magnitudes of each of those multiplied together times the cosine of the angle between them. And we have all that already because they just give it to us. So we just need to come over here and plug all that in now. So we know that the magnitude of a is 80. The magnitude of the is 50. And then, you know, the angle between them is three pi fourth. So now we just multiply everything together. Uh, so 80? Yeah. Times 40 would be armed up 40 80 times. 50 should be 4000. Co sign of three pi force. Well, that is where co sign is negative. It would be negative. Route two or two and then simplifying the two in the 4000 would give us 2000, so this would be negative 2000 route to. So this is going to be our product

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