<Dd> a 2 = a − a 1 (\ displaystyle \ mathbf (a) _ (2) = \ mathbf (a) - \ mathbf (a) _ (1)) </Dd> <Dl> <Dd> a 2 = a − a ⋅ b b ⋅ b b . (\ displaystyle \ mathbf (a) _ (2) = \ mathbf (a) - (\ frac (\ mathbf (a) \ cdot \ mathbf (b)) (\ mathbf (b) \ cdot \ mathbf (b))) (\ mathbf (b)).) </Dd> </Dl> <Dd> a 2 = a − a ⋅ b b ⋅ b b . (\ displaystyle \ mathbf (a) _ (2) = \ mathbf (a) - (\ frac (\ mathbf (a) \ cdot \ mathbf (b)) (\ mathbf (b) \ cdot \ mathbf (b))) (\ mathbf (b)).) </Dd> <P> The scalar projection a on b is a scalar which has a negative sign if 90 <θ ≤ 180 degrees . It coincides with the length c of the vector projection if the angle is smaller than 90 ° . More exactly: </P>

What is the meaning of a projection of one vector to another