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aaronfue
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Homework Statement
I would appreciate it if someone could verify my answer.
Find a vector-valued function that represents the plane x+y+z=6.
2. The attempt at a solution
r(u,v) = ui + vj + (6-u-v)k
Thanks!
aaronfue said:Homework Statement
I would appreciate it if someone could verify my answer.
Find a vector-valued function that represents the plane x+y+z=6.
2. The attempt at a solution
r(u,v) = ui + vj + (6-u-v)k
Thanks!
Dick said:That should do it. u+v+(6-u-v)=6.
A vector valued function is a mathematical function that takes in one or more inputs and returns a vector as its output. The components of the vector can be either real numbers or complex numbers.
A regular function takes in one or more inputs and returns a single value as its output. A vector valued function, on the other hand, returns a vector as its output, which can have multiple components.
The domain of a vector valued function is the set of all possible input values for which the function is defined. The range is the set of all possible output vectors that can be obtained from the function.
A vector valued function can be graphed by plotting the individual components of the vector as separate functions on a coordinate plane. Each component will have its own graph, and the combination of all the graphs will form the graph of the vector valued function.
Yes, a vector valued function can be differentiated component-wise, meaning that each component of the vector can be differentiated separately. The result will be a vector of derivatives, also known as the gradient vector.