Two adjacent sides of a parallelogram ABCD are `2hati+4hatj -5 hatkand hati+2hatj+3hatk`. Then the value of `|vec(AC)xxvec(BD)|` is

Options

A. `20sqrt5`
B. `22sqrt5`
C. `24sqrt5`
D. `26sqrt5`

Answer

b

Explanation

`|vec(AC) xx vec(BD)|=2 |vec(AB)xxvec(AD)|`
`2|{:(hati,hatj,hatk),(2,4,-5),(1,2,3):}|`
`|2[hati(12+10)-hatj (6+5)+hatk (4-4)]|`
`|2[22hati -11 hatj]|`
`22 |[2hati - hatj]|`
`22xx sqrt5`