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 (â2, 3, 1) and contains the line of intersection of the planes *x* + *y* â *z* = 5 and 3*x* â *y* + 5*z* = 4

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

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

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

5) Find an equation for the plane consisting of all points that are equidistant from the points (7, 0, â2) and (9, 6, 0).

6) Find the distance from the point to the given plane : (1, â9, 5), 3*x* + 2*y* + 6*z* = 5

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

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 (â2, 3, 1) and contains the line of intersection of the planes *x* + *y* â *z* = 5 and 3*x* â *y* + 5*z* = 4

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

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

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

5) Find an equation for the plane consisting of all points that are equidistant from the points (7, 0, â2) and (9, 6, 0).

6) Find the distance from the point to the given plane : (1, â9, 5), 3*x* + 2*y* + 6*z* = 5

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