Please solve this vector question.

Question

What is the volume of the parallelogram defined by the vectors A(4,2,3) B(8,-1,-4) and C(11,3,-2)?

Answer 1

If this is a parallelogram, we are calculating area and not volume.A(4,2,3) B(8,-1,-4) and C(11,3,-2)

B - A = (8,-1,-4) - (4,2,3) = (4, -3, -7)

C - A = (11,3,-2) - (4,2,3) = (7, 1, -5)

We then calculate the cross-product

The determinant of

i j k

4 -3 -7

7 1 -5

is

22i - 29j + 25k

The magnitude of (22, -29, 25) is (22² + (-29)² + 25²)^1/2 = √1950 = 5√78 or 44.1588043316392