Question

Find the area of the parallelogram with one corner at P1 and adjacent sides

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

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.

The vectors are and

The position vectors and are adjacent sides of a parallelogram.

The area of the parallelogram is

The area of the parallelogram is

Solution :

The area of the parallelogram is