The area of the parallelogram whose diagonals are  and  is:

Concept:

Area of a parallelogram with vectors  and  as its diagonals is given by: .

Cross Product: For two vectors  and , their cross product is given by:

.

The magnitude  of a vector  is given by: .

Calculation:

The given diagonals of the parallelogram are  and .

Using the formula for the area of a parallelogram whose diagonals  and  are given, we get:

= 

= 

= 

= 

= 

= .

Additional Information

Area of a parallelogram with vectors  and  as its sides is given by: .

For two vectors  and  at an angle θ to each other:

• Dot Product is defined as: .
• Cross Product is defined as: , where  is the unit vector perpendicular to the plane containing  and .