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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) $\mid a \mid \cdot (b + c)$

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

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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

Oklahoma State University

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