Question: is the cross product of two normalized vectors normalized

Answer: Yes, In mathematics and vector algebra, the cross product or vector product (occasionally directed area product to emphasize the geometric significance) is a binary operation on two vectors in three-dimensional space ( R 3 ) (\displaystyle \left(\mathbb (R) ^(3)\right)) and is denoted by the symbol × (\displaystyle \times ) . Given two linearly independent vectors a (\displaystyle \mathbf (a) ) and b (\displaystyle \mathbf (b) ) , the cross product, a × b (\displaystyle \mathbf (a) \times \mathbf (b) ) , is a vector that is perpendicular to both a (\displaystyle \mathbf (a) ) and b (\displaystyle \mathbf (b) ) and thus normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. It should not be confused with dot product (projection product).