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Question
In each of the following, express vector x in terms of vector u and vecto v. (You make click on each diagram for a larger view.)

I have absolutely no idea what to do for this problem

From the first figure, the endpoint of the vector x lies on the midpoint of the line between the endpoint of the vectors u and v. If the line from the tip of u to the tip of v is the vector w, then by vector addition, v = u + w, or w = v - u. The vector from the tip of u to the tip of x is (1/2)w = (1/2)(v - u). Therefore, x = u + (1/2)w.

For the 2nd figure, the relations are the same with v' = -v.

Randy

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#### randy patton

##### Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

##### Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

Education/Credentials
M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

Past/Present Clients
Also an Expert in Oceanography