" 10."ax+cy-ac-xy

Let a,b,c be real numbers with a^2 + b^2 + c^2 =1. Show that the equation |[ax-by-c,bx+ay,cx+a],[bx+ay,-ax+by-c,cy+b],[cx+a,cy+b,-ax-by+c]|=0 represents a straight line.

Let a,b,c be real numbers with a^2 + b^2 + c^2 =1 . Show that the equation |[ax-by-c,bx+ay,cx+a],[bx+ay,-ax+by-c,cy+b],[cx+a,cy+b,-ax-by+c]|=0 represents a straight line.

If ab + xy - xb = 0 and bc + yz - cy = 0, then is x/a+c/z equal to ?

[[a, b, ax + byb, c, bx + cyax + by, bx + cy, 0]] = (b ^ (2) -ac) (ax ^ (2) + 2bxy + cy ^ (2))

det[[ Prove that: ,b,ax+bya,c,bx+cyax+by,bx+cy,0]]=(b^(2)-ac)(ax^(2)+2bxy+cy^(2))

Prove that the bisectors of the angle between the lines ax^2+acxy+cy^2=0 and (3+1/c)x^2+xy+(3+1/a)y^2=0 are always the same .

Prove that the bisectors of the between the lines ax^2+acxy+cy^2=0 and (3+1/c)x^2+xy+(3+1/a)y^2=0 are always the same .

Prove that the bisectors of the angle between the lines ax^2+acxy+cy^2=0 and (3+1/c)x^2+xy+(3+1/a)y^2=0 are always the same .

Prove that the bisectors of the between the lines ax^2+acxy+cy^2=0 and (3+1/c)x^2+xy+(3+1/a)y^2=0 are always the same .