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Find the trace lines of the plane E.
Published on November 27, 2024
Linear-Algebra
The solution finds the trace lines of a plane by setting one coordinate to zero and solving for the other two coordinates in terms of the remaining parameter. This results in parametric equations for the trace lines in the xy, xz, and yz planes.
Question
bitte a) lösen
Answer
Here’s how to find the trace lines (Spurgeraden) for the plane E in part a):
Understanding Trace Lines
A trace line is the intersection of a plane with a coordinate plane (xy, xz, or yz). To find them, we set one of the coordinates to zero.
Given Equation
The plane E is given by the vector equation:
1. x-y Trace (z = 0)
Set z = 0:
Substitute this back into the vector equation for
This is the equation of the x-y trace line.
2. x-z Trace (y = 0)
Set y = 0:
Substitute this back into the vector equation for
This is the equation of the x-z trace line.
3. y-z Trace (x = 0)
Set x = 0:
Substitute this back into the vector equation for
This is the equation of the y-z trace line.
Final Answer: The final answer is