with(linalg): a := sqrt(2)/2: x := 2*t; y:= a + (1-3*a)*t; z:= a +(2-3*a)*t; tstar := solve(x^2+y^2+z^2 = 1, t); expand(x^2+y^2+z^2 = 1); sort(%,t); collect(%,t); L := t -> vector([0,a,a]) + t*vector([2,1-3*a,2-3*a]); P1 := L(0); P2 := L(1/3); P3 := vector([0,0,1]); evalm(P2); len := vec -> sqrt(innerprod(vec,vec)); area := len(crossprod(P2-P1,P3-P1))/2; evalf(area);