By the ‘angle between a vectorand a plane’ we mean the angle between the vectorand a particular vector drawn in the plane. In the plane there are actually many vectors, and the particular vector we pick is the vector that makes the smallest angle with the vectorThis is the angle shown as in the diagram below.
If the equation of a planethen the normal to the plane is the vector and we can find the angle betweenandusingSinceis normal to the plane so
Example: find the angle between the vectorand the plan
The normal vector to the plane isso