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

Kyran Hudson 2021-01-05 Answered
Find a set of vectors that spans the plane $P1:2x+3y-z=0$
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SoosteethicU

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