Question

The diagonals of a parallelogram are given by `veca = 2hati - hatj + hatk and vecb = hati + 3hatj - hatk`. Find the area of the parallelogram.

Answer 1

Diagonals of a parallelogram are 

`veca = 2hati - hatj + hatk`

`vecb = hati + 3hatj - hatk`

`|veca xx vecb| = |(2hati - hatj + hatk) xx (hati + 3hatj - hatk)|`

= `|(hati,  hatj, hatk), (2, -1, 1), (1, 3, -1)|`

= `|hati(1 - 3) - hatj(-2-1) + hatk(6 + 1)|`

=`|-2hati + 3hatj + 7hatk|`

Since the given vectors are diagonals of the parallelogram, the area is given by the formula:

Now, the area of the parallelogram = `1/2 xx |veca xx vecb|`

= `1/2 sqrt((-2)^2 + (3)^2 + (7)^2)`

= `1/2 sqrt(4 + 9 + 49)`

= `1/2 sqrt(62)` sq. units

= `sqrt(62)/2` sq. units