Question

Find the area of parallelogram whose diagonals are determined by the vectors `bar"a" = 3hat"i" - hat"j" - 2hat"k"` and `bar"b" = - hat"i" + 3hat"j" - 3hat"k"`.

Answer 1

Given: `bar"a" = 3hat"i" - hat"j" - 2hat"k"` , `bar"b" = - hat"i" + 3hat"j" - 3hat"k"`.

∴ `bar"a" xx bar"b" = |(hat"i",hat"j",hat"k"),(3,-1,-2),(-1,3,-3)|`

`= (3 + 6)hat"i" - (- 9 - 2)hat"j" + (9 - 1)hat"k"`

`= 9hat"i" + 11hat"j" + 8hat"k"`

and `|bar"a" xx bar"b"| = sqrt(9^2 + 11^2 + 8^2) = sqrt(81 + 121 + 64) = sqrt266`

Area of the parallelogram having diagonals `bar"a"` and `bar"b" = 1/2 |bar"a" xx bar"b"| = 1/2sqrt266` sq units.