<P> When θ is not known, the cosine of θ can be computed in terms of a and b, by the following property of the dot product a b: </P> <Dl> <Dd> a ⋅ b a b = cos ⁡ θ (\ displaystyle (\ frac (\ mathbf (a) \ cdot \ mathbf (b)) (\ mathbf (a) \, \ mathbf (b))) = \ cos \ theta \,) </Dd> </Dl> <Dd> a ⋅ b a b = cos ⁡ θ (\ displaystyle (\ frac (\ mathbf (a) \ cdot \ mathbf (b)) (\ mathbf (a) \, \ mathbf (b))) = \ cos \ theta \,) </Dd> <P> By the above - mentioned property of the dot product, the definition of the scalar projection becomes </P>

Orthogonal projection of a vector onto a plane