Question

Find the area of the parallelogram whose adjacent sides are determined by the vector `veca = hati - hatj + 3hatk` and `vecb = 2hati - 7hatj + hatk`.

Answer 1

`veca = hati - hatj + 3hatk, vecb = 2hati - 7hatj + hatk`

Here, `veca xx vecb = |(hati, hatj, hatk), (2, 3, 4), (4, 6, 8)|`

= `hati(-1 + 21) - hatj(1 - 6) + hatk(-7 + 2)`

= `20hati + 5hatj - 5hatk`

∴ Area of parallelogram = `veca xx vecb`

= `|veca xx vecb| = sqrt((20)^2 + 5^2 + 5^2)`

`= sqrt450`

`= 15sqrt2` square unit.