how to find if ax+by+cz+d=0 is an equation of a line or a plane.
2007-01-06 16:00:52 · 5 answers · asked by askance 4 in Science & Mathematics ➔ Mathematics
Actually, the coefficients can be 0. For example, x + 0y + 0z = 0 is the equation of the yz-plane.
In three dimensions, that equation would always represent a plane, unless all of the coefficients are zero. To represent a line, you need another parameter, or you have to describe it as an intersection of two planes.
2007-01-06 16:47:15 · answer #1 · answered by bictor717 3 · 1⤊ 0⤋
The geometrical representation of the equation would be a plane if all the coefficients of the variables x, y and z are real and not zero.
ADDED: when the equation is x+0y+0z=0, it is the same as x=0. And x=0 is a line not a plane. Thank you.
2007-01-06 16:39:03 · answer #2 · answered by supermmm 1 · 1⤊ 0⤋
3 variables thus a plane. ( even if c = 0 )
if you intersect this equation with aanother, you will get a line ( or empty set )
2007-01-06 17:37:19 · answer #3 · answered by gjmb1960 7 · 1⤊ 0⤋
well, you're dealing with three kind of variables (x, y and z) so this must be the equation of a plane, 'cause each variable is located in one axis.. so you have three dimensions there
:)
2007-01-06 16:04:58 · answer #4 · answered by IQ DOSON 2 · 1⤊ 0⤋
well in a plane, variable x and y are only the variables, but in your case, z is included. then, you are meeting three variables in a plane..
^_^
2007-01-06 16:20:48 · answer #5 · answered by richard 2 · 0⤊ 0⤋