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Which of the following expressions are meaningful? Which are meaningless? Explain.(a) $ (a \cdot b) \cdot c $ (b) $ (a \cdot b) c $(c) $ \mid a \mid (b \cdot c) $ (d) $ a \cdot (b + c) $(e) $ a \cdot b + c $ (f) $ \mid a \mid \cdot (b + c) $

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a) Meaningless.b) Meaningful.c) Meaningful.d) Meaningful.e) Meaningless.f) Meaningless.

02:24

Madi Sousa

Calculus 3

Chapter 12

Vectors and the Geometry of Space

Section 3

The Dot Product

Vectors

Johns Hopkins University

Campbell University

Harvey Mudd College

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.

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Which of the following exp…

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1. Which of the following …

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Explain why each of the fo…

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For numbers a and $b,$ det…

I'm assuming that a B and c are vectors. So when you do the dot product, that's a number. Alright. So here we have a number and we're trying to dot it with a vector. That doesn't make sense. Okay, so um I forgot what it asked. Doesn't make sense. No. No one has but no. Okay. Okay. The next one says dot A and B and then multiplied by a vector. Yes, that makes sense. Because it's a number of times a vector kids at third one magnitude of a. That's a number. How big is the vector? How long is the vector? And you're multiplying it by be dot C which is also a number. So it's a number of times a number. Yes, that makes sense. All right. When you add two vectors that's a vector. So this one is a vector dotted with a vector. Yes, that makes sense. Mhm. Okay. Next 18 dot be That's a number plus a vector. No, that doesn't make any sense. Alright, The next one is a magnitude which is a number and a vector. And we're dotting a number in a vector. No, that doesn't make any sense. Okay. I hope that helps

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