# Vectors : Dot Products and Planes and Distance from a Point

1) a = (1, 2, -2); ||b|| = 6. What choice of b will make the dot product a . b the least possible?

2) The plane P pass through the point M (2, 3, 1) and is parallel to vectors u = (1, -1, 4) and v = (2, 1, 0).

Find the distance from the point N (3, 2, 4) to the plane P.

3) Find an equation of the plane that passes through (1, 2, 3), (0, 1, 0) and (2, 0, 1).