> solve({3*x-2*y+5*z=12,x=3*t,y=-2*t,z=5*t});solve(3*x-2*y+5*z=12,z);
> with(plots):with(plottools):a:=arrow([18/19,-12/19,30/19],[3,-2,5],.4,.4,.2,color=green):b:=plot3d((-3*x+2*y+12)/5,x=-3..3,y=-3..3,scaling=constrained):display(a,b);
> e:=exp(1);f:=(x,y)->3*(1-x)^2*e^(-x^2-(y+1)^2)-10*(x/5-x^3-y^5)*e^(-x^2-y^2)-(1/3)*e^(-(x+1)^2-y^2);
> a:=plot3d(f(x,y),x=-3..3,y=-3..3,style=wireframe):a;
> b:=spacecurve([1/5,y,f(1/5,y)],y=-3..3,thickness=8,color=green):b;
> c:=spacecurve([x,3/2,f(x,3/2)],x=-3..3,thickness=8,color=blue):display(a,b,c);
> with(linalg):u:=vector([1,2,3]);v:=vector([3,1,3]);
> n:=scalarmul(v,1/norm(v,2));
> projection:=scalarmul(n,dotprod(u,n));dotprod(u,n);
> f:=(x,y)->sin(x)*sin(y);
> f:=(x,y)->x^2+y^2;
> a:=gradplot(f(x,y),x=-3..3,y=-3..3,scaling=constrained):a;
> b:=contourplot(f(x,y),x=-3..3,y=-3..3,scaling=constrained):b;
> display(a,b);
> with(linalg);
> 
> grad(x^2+y^2,[x,y]);
> grad(x^2+y^2,[y,x]);
> f:=(x,y,z)->x^2+3*x*y+2*z;at:={x=2,y=0,z=-1};u:=vector([2,1,-2]);
> n:=normalize(u);
> dfu:=dotprod(grad(f(x,y,z),[x,y,z]),n);
> subs(at,dfu);
>