Question

You know its nice to get the answer, but I'm trying to learn these so please explain it in detail please.

1) Find an equation of the plane: The plane that passes through the point (−2, 3, 1) and contains the line of intersection of the planes x + y − z = 5 and 3x − y + 5z = 4

2) Find an equation of the plane: The plane that passes through the line of intersection of the planes x − z = 2 and y + 4z = 3 and is perpendicular to the plane x + y − 2z = 5

3) Find the point at which the line intersects the given plane: x = 4 − t, y = 3 + t, z = 2t; x − y + 3z = 5

4) Find the cosine of the angle between the planes : x + y + z = 0 and x + 4y + 3z = 7

5) Find an equation for the plane consisting of all points that are equidistant from the points (7, 0, −2) and (9, 6, 0).

6) Find the distance from the point to the given plane : (1, −9, 5), 3x + 2y + 6z = 5

7) Find the distance between the given parallel planes. 3x − 2y + z = 9, 6x − 4y + 2z = 3