[Math] Area of parallelogram given diagonals in vector form

Question

Q: If the diagonals of a parallelogram are:

D1: i+j-2k
D2: i-3j+4k

Then find area of the parallelogram.

My attempt:
Since lengths of diagonals is different, the parallelogram can be a rhombus.
So area is 1/2*|D1|*|D2|.
Is this correct?

Answer 1

No, this is incorrect. The area of a parallelogram is $$|\triangle|=\frac{1}{2}||D_1 \times D_2||$$ Here $\times$ denotes the cross product of the the two diagonals. Then you must take the magnitude of that vector in absolute terms, hence the double modulus signs. Intuitively, it makes sense since area is a vector quantity and the formula you are using suggests that area is a scalar quantity.