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anonymous
 one year ago
Find a parametric representation for the surface. (Enter your answer as a commaseparated list of equations. Let x, y, and z be in terms of u and/or v.)
The plane through the origin that contains the vectors i − j and j − k
anonymous
 one year ago
Find a parametric representation for the surface. (Enter your answer as a commaseparated list of equations. Let x, y, and z be in terms of u and/or v.) The plane through the origin that contains the vectors i − j and j − k

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I got \[r=<u,v,uv>\] the computer didn't accept it though

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0did you for for \(\vec r=<\vec u,\vec v,−\vec u−\vec v>\) just because this is \(\pi: \ x+y+z = 0\)??

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yea thats what I did

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Sorry I did the cross product to get r=i+j+k then subed in the values for x y z

IrishBoy123
 one year ago
Best ResponseYou've already chosen the best response.0i see where you are coming from and perhaps the problem is with data entry as often happens on websites but maybe you could also approach it differently, more simply even, using the basic info they have given you. Info given = "The plane through the origin that contains the vectors i − j and j − k" so you know that any point (x,y,z) can be found by starting at the origin (0,0,0) and using the given vectors, ie \(<x,y,z> = <0,0,0> + u <1,1,0> + v<0,1,1> \) \( = u <1,1,0> + v<0,1,1>\) for example, we know (2,3,5) is on plane, thus testing \[\left(\begin{matrix}2 \\ 3 \\5 \end{matrix}\right) = u \left(\begin{matrix}1 \\ 1 \\0 \end{matrix}\right) + v \left(\begin{matrix} 0 \\ 1 \\1 \end{matrix}\right) \] \(\implies u = 2, v = 5\) so for "(Enter your answer as a commaseparated list of equations." you might try: x = u, y =  u + v, z = v i think you'd be fine with a human marking system :p
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