Vectors

Step 1: The area of the parallelogram is given by the magnitude of the cross product of the vectors and :

Step 2: Compute the cross product :

Step 3: Expand the determinant: Step 4: Find the magnitude of the cross product: \bigskip

Step 1: Find and

Given:
Step 2: Find a vector perpendicular to both


Step 3: Compute the cross product


Step 4: Find the magnitude of


Step 5: Find the unit vector


Step 6: Final Answer

Note: The negative of this vector is also a unit vector perpendicular to both given vectors.