We have,
Let ABCD be a parallelogram.
In ABCD,
Now, by triangle law of addition, we get
Adding equations (i) and (ii), we get
We know that,
Vector area of parallelogram ABCD is given by,
Now, we need to find the area of parallelogram whose diagonals are \(2 \hat i - \hat j + \hat k \,and\, \hat i + 3 \hat j - \hat k.\)
We have already derived the relationship between area of parallelogram and diagonals of parallelogram, which is