Question

Find the area of the parallelogram with vertices P1, P2, P3, and P4.

P1 = (1, 1, 2),    P2 = (1, 2, 3),     P3 = (- 2, 3, 0),     P4 = (- 2, 4, 1)

Answer 1

Step 1 :  

If the initial point is and the terminal point is , then

the position vector is

Area of the parallelogram :

If u and v are adjacent sides of a parallelogram, then the area of the parallelogram is .

Step 2 :

The points are and .

The position vector is

Substitute the points and in v.

Substitute the points  and in v.

Step 3 :

The position vectors and are adjacent sides of a parallelogram.

The area of the parallelogram is

Solution :

The area of the parallelogram is square units.