o:=matrix([0,0,0]):

a:=matrix([4,2,-1]):

v:=matrix([3,1,-4]):

w:=matrix([2,3,-5]): a,v,w

ebene:=a+ r*v+s*w

apkt:=plot::Point3d(a):

av:=plot::Arrow3d(o,a):

vv:=plot::Arrow3d(a,a+v, LineColor=[0,1,0]):

ww:=plot::Arrow3d(a,a+w):

eb:=plot::Surface(ebene,r=-5..5,s=-5..5,

          ViewingBox=[-5..8,-5..6,-8..5]):

plot(eb,apkt,ww,vv,av, Scaling=Constrained)

vw:=linalg::scalarProduct(v,w);

lvq:=linalg::scalarProduct(v,v);

lwq:=linalg::scalarProduct(w,w);

cosi:=vw/sqrt(lvq*lwq); float(cosi);

float(arccos(cosi)*180/PI)

n:=linalg::crossProduct(v,w);

nv:=plot::Arrow3d(a,n, LineColor=[1,0,0]):

plot(eb,nv,av,vv,ww,Scaling=Constrained)

p:=matrix([x,y,z]):

ehess:=(linalg::scalarProduct((p-a),n)=0)

eh:=plot::Implicit3d(ehess,x=-5..8,y=-5..5,z=-8..5):

plot(eh,av,nv,vv,ww, Scaling=Constrained)