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Two adjacent sides of a parallelogram AB...

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

A

`20sqrt5`

B

`22sqrt5`

C

`24sqrt5`

D

`26sqrt5`

Text Solution

Verified by Experts

The correct Answer is:
b
`|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`
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