Find a set of vectors that spans the plane P1: 2x + 3y -z = 0

Vectors and spaces
asked 2021-01-05
Find a set of vectors that spans the plane \(\displaystyle{P}{1}:{2}{x}+{3}{y}-{z}={0}\)

Answers (1)

Note that if \(\displaystyle{\left({x},{y},{z}\right)}∈{P}{1}\) then \(\displaystyle{2}{x}+{3}{y}−{z}={0}.\) Therefore we have \(\displaystyle{z}={2}{x}+{3}{y}\)
It follows that the vectors (1,0,2), (0,1,3) spans the plane P1.

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