Question

find the equation of the plane through the point (4,2,1) and (2,1,-1) and making angle π/4 with the plane x-4y+z-9=0

Answer 1

let plane be Ax+By+Cz+D=0
vector along plane =(2,1,2)

so 2.A + B + 2C =0
now satisfy the point to get 2 another equations
4A+2B+C+D=0
2A + B - C +D =0
and since it makes angle 45
so, Cos45 =[ A.1 -4.B + C]÷[√(A^2 + B^2 + C^2)×√(1^2 + 4^2 + 1^2)]
4 equation 4 variables you can solve it now