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Algebra/More on dot product..
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I just want to thankyou for your previous response to my question.
My question is as follows: If A.B = A.C then does B=C ? I can easily just let A = (0,1,0), B = (1,0,0) and C= (0,0,1) which means that A.B = A.C = 0 and shows that B (does not equal) C. Is there a more valid way to show this?
The question does lead on to say: Show with a sketch what is the condition that the three vectors satisfy. I don't understand what the question is asking me to prove here. Thank you in advance!
Hello Jay,
Your example is definitely enough to prove what you want to but yes, there should be a, not more VALID, but more GENERAL way to do it. Try writing the condition A.B=A.C without putting any numbers, for example: A=(a1,a2,a3), B=(b1,b2,b3), etc. and see where this gets you. You may also want to try it using the other form of the dot product: A.B=|A||B|cos(angleAB).
I think what the second part is asking is that you write down (and draw) what vectors A,B and C must satisfy so that (A.B=A.C).
Hope this helps,
David
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Answers by Expert:
David Montiel
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PLEASE READ THIS BEFORE POSTING YOUR QUESTION: While I am glad to offer HELP with problems, I refuse to SOLVE problems. There is a difference. Please do not just copy a question from a texbook or assignment. I WILL REJECT IT. I will only accept questions if, in addition to the statement of the problem, you describe in detail what you have tried so far in order to solve it, and what exactly is the problem you are encountering. In other words where/why are you stuck? I can answer questions at the level of the first couple of undergraduate years (in science and engineering) or below. You can ask me about algebra, trigonometry, basic probability and statistics, calculus, vector calculus, differential equations and Fourier analysis. I will not answer advanced (at the graduate level) math questions. Questions in Spanish are also welcome.
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