Questionfind the eque of the plare that contains to the line: $x+t, y=1, z=-1+t$ and perpend to the plane $\pi: \quad 3 x-y+z-7=0$

Studdy Solution
Use a point on the line and the normal vector to find the equation of the plane. A point on the line is $(0, 1, -1)$.
The equation of the plane is given by:
$$n_1(x - x_0) + n_2(y - y_0) + n_3(z - z_0) = 0$$
Substitute the point $(0, 1, -1)$ and the normal vector $\langle 1, -2, -1 \rangle$:
$$1(x - 0) - 2(y - 1) - 1(z + 1) = 0$$
Simplify:
$$x - 2y + 2 - z - 1 = 0$$ $$x - 2y - z + 1 = 0$$
The equation of the plane is:
$$\boxed{x - 2y - z + 1 = 0}$$