Math
The Dot Product

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The dot product is defined in two dimensions as (a₁, b₁) (a₂, b₂) = a₁a₂ + b₁b₂

 

or in three dimensions (a₁, b₁, c₁) (a₂, b₂, c₂) = a₁a₂ + b₁b₂ + c₁c₂

Note that the dot product is a scalar value and not another vector.

 

If then the vectors are perpendicular.  We can find the equation of a plane that is perpendicular to a vector using this fact.  If we want to find the equation of the plane containing the point P = (-1, 5, 2) perpendicular to the vector , we let R = (x, y, z) be any point in the plane and solve the equation