Calculate the area of a paralleogeram whose adjcent sides are given by the vectors :
` vec A = hat i- 2 hat j= 3 hat k` , and ` vec B = 2 hat I = 3 hat j- hat k`.

Explanation

Area of the parallelogram ` = | vec A xx vec B|`
Here, ` vec A xx vec B= | ( hat I, hat j, hat k), (1, -2, 3), ( 2, 3, -1,)|`
` = hat I ( 2 - 9) + hat j ( 6 + 1) + hat k ( 3 + 4)`
` =- 7 hat i+ 7 hat j + 7 hat k`
:. Area of paralelogram
` |vec Axx vec B| = sqrt (-7)^2 + (1) + (7) + (7)^2)`
` = 7 sqrt 3 ` units of area.