Question

Equation of the line of projection of the line 3x - y + 2z -1 = 0 = x + 2y - z - 2 on the plane 3x + 2y +z = 0

Answer 1

3x + 2y + z = 0, 3x - 8y + 7z + 4 = 0

Answer 2

The line of projection of a line L onto a plane P is the intersection of P and the plane (P') containing L and perpendicular to P. The plane P' is found by taking the general equation of a plane containing L ($P_1 + \lambda P_2 = 0$) and using the condition that its normal vector is orthogonal to the normal vector of P, solving for $\lambda$. Substituting $\lambda$ back gives P'. The line of projection is then expressed as the system of equations for P and P'.