Take two - but it's Mma - not W|A

Show[{ParametricPlot3D[\[Alpha] {0, 1, 3} + \[Beta] {1, 1/2, -1/3}, {\[Alpha], -2, 2}, {\[Beta], -3, 3},

DisplayFunction -> Identity],

ParametricPlot3D[\[Alpha] {1, -1/3, 1/5} + \[Beta] {-1/2, 1, -1}, {\[Alpha], -2, 2}, {\[Beta], -3, 3},

DisplayFunction -> Identity]}, DisplayFunction -> $DisplayFunction]

in W|A you will find real entertainment, saying to it

plot two planes through the origin

W|A displays a fighters ranking ... do not know about what

two planes through the origin

gives valuable linguistic information

Show[{ParametricPlot3D[\ {0, 1, 3} + \ {1, 1/2, -1/3}, {\, -2, 2}, {\, -3, 3},

DisplayFunction -> Identity],

ParametricPlot3D[\ {1, -1/3, 1/5} + \ {-1/2, 1, -1}, {\, -2, 2}, {\, -3, 3},

DisplayFunction -> Identity]}, DisplayFunction -> $DisplayFunction]

says input too long ... so do yourself a favour and use Mma. Try this

plane intersects another one

says "... bites the dust" --- Freddy calls back ... great but not in the field of linear algebra or plane geometry.