The vector-valued function representing the plane defined by the equation x+y+z=6 is correctly expressed as r(u,v) = ui + vj + (6-u-v)k. This formulation ensures that the sum of the components equals 6, confirming the validity of the solution. The function utilizes parameters u and v to describe the plane in three-dimensional space effectively.
PREREQUISITESStudents in mathematics, particularly those studying multivariable calculus, as well as educators and anyone interested in understanding vector-valued functions and their applications in geometry.
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.