 IsOnObject - Maple Help

geom3d

 IsOnObject
 Test if a point, a list, or a set of points is on a given object Calling Sequence IsOnObject(f, obj, cond) Parameters

 f - point, list or set of points obj - line, plane, or sphere cond - (optional) name Description

 • The routine returns true if the point f or the list/set of points f is on object obj; false if it is not; and FAIL if it is unable to reach a conclusion.
 • In case of FAIL, if the third optional argument is given, the condition that makes f on object l is assigned to this argument. It will be either of the form $\mathrm{expr}=0$ or of the form $&\mathrm{and}\left(\mathrm{expr_1}=0,...,\mathrm{expr_n}=0\right)$ where expr, expr_i are maple expressions.
 • The command with(geom3d,IsOnObject) allows the use of the abbreviated form of this command. Examples

 > $\mathrm{with}\left(\mathrm{geom3d}\right):$

Find the equation of the plane through the line (3*x-4*y+5*z=10, 2*x+2*y-3*z=4) and parallel to the line x=2*y=3*z

 > $\mathrm{point}\left(o,0,0,0\right):$
 > $\mathrm{line}\left(\mathrm{l1},\left[o,\left[1,\frac{1}{2},\frac{1}{3}\right]\right]\right):$
 > $\mathrm{plane}\left(\mathrm{p1},3x-4y+5z=10,\left[x,y,z\right]\right):$$\mathrm{plane}\left(\mathrm{p2},2x+2y-3z=4,\left[x,y,z\right]\right):$
 > $\mathrm{line}\left(\mathrm{l2},\left[\mathrm{p1},\mathrm{p2}\right]\right):$
 > $\mathrm{plane}\left(p,\left[\mathrm{l2},\mathrm{l1}\right]\right):$

check if line l2 lies in the plane p, line l1 is parallel to plane p

 > $\mathrm{IsOnObject}\left(\mathrm{FixedPoint}\left(\mathrm{l2}\right),p\right);$$\mathrm{AreParallel}\left(\mathrm{l2},p\right);$$\mathrm{AreParallel}\left(\mathrm{l1},p\right)$
 ${\mathrm{true}}$
 ${\mathrm{true}}$
 ${\mathrm{true}}$ (1)