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Finding the Acute Angle Between a Vector and a Plane

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 asin the diagram below.

If the equation of a planethen the normal to the plane is the vectorand we can find the angle betweenandusingSinceis normal to the planeso

Example: find the angle between the vectorand the plan

The normal vector to the plane isso

So thatand