Vectors

Let the two forces be and , and suppose the resultant is perpendicular to .
Using the formula for resultant: But since , we can also use: Hence, Set and solve for or . After simplification, we get:

The area of a parallelogram formed by two vectors and is given by the magnitude of the cross product of the vectors: To calculate the cross product , we use the determinant method: Expanding the determinant: Solving each 2x2 determinant: Now, calculate the magnitude of the cross product:
Thus, the area of the parallelogram is square units.