Advanced Math/Vectors

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Expert: - 7/27/2010


Question

The Problem
The problem is written with diagram in the picture attached. I've been working on this problem for the past 4 days. I know the answer, just not how to get to the answer. How might I do this?

Answer
|CE| = (2/5)|CB| , so the vector CE is (2/5)(B-C)

|AD| = (2/3)|AB| , so the vector AD is (2/3)(B-A)

We then have vector AE = vector AC + vector CE = C-A+(2/5)(B-C) = (2/5)B +(3/5)C - A

Q is the midpoint of CD , so vector AQ = (1/2)(vector AC + vector AD)

Then vector AQ = (1/2)[(C-A) + (2/3)(B-A)] = (1/3)B + (1/2)C - (5/6)A

To summarize :

AE = (2/5)B +(3/5)C - A

AQ = (1/3)B + (1/2)C - (5/6)A


So vector  AQ = (5/6)AE , as you can easily check.

So c = 5/6 = |AQ|/|AE|

Socrates

Expertise

I can answer any questions from the standard four semester Calulus sequence. Derivatives, partial derivatives, chain rule, single and multiple integrals, change of variable, sequences and series, vector integration (Green`s Theorem, Stokes, and Gauss) and applications. Pre-Calculus, Linear Algebra and Finite Math questions are also welcome.

Experience

Ph.D. in Mathematics and many years teaching undergraduate courses at three state universities.

Education/Credentials
B.S. , M.S. , Ph.D.

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