1. find the distance of point P from the line AB whith A (1,2,0). B (3,0,-2)
d = abs((P-B)^(A-B))/(A-B)
this formula is applicable in any dimension
Resp. d=1.633
2. find the distance between two lines, say AB and CD
E = (A-B)^(C-D)
d = reject(A-C),E) orthogonal rejection of A-C outside the plane E = (A-B)^(C-D)
this formula is applicable in any dimension`
3. find the angle ABC with A (5,9,0). B(2,3,0) C(8,3,0)
angle = |<log((A-B)/(C-B))>2| with <A,2> = grade2(A)
Cl(3)
A=5e1+9e2. B=2e1+3e2 C=8e1+3e2
q=gp((A-B),inverse(C-B))
angle=magnitude(grade(log1(q),2))
resp. angle=1.107
4. find a rotationn sending a unit vector x to the unit vector y.
y1 = u x1/u with u = sqrt(x1/y1)
Cl(3)
x=e1-e2-e3. y=e1+e2-e3
x1=normalize(x). y1=normalize(y)
u=sqrt1(gp(x1,inverse(y1)))
y1=gp(u,gp(x1,inverse(u)))
5.