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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).

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Vectors, Dot Products and Planes and Distance from a Point are investigated.

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