The vectors from origin to the points A and B are `veca=2hati-3hatj+2hatkandvecb=2hati+3hatj+hatk` respectively , then area of triangle OAB is

Options

A. 340
B. `sqrt25`
C. `sqrt229`
D. `(1)/(2)sqrt229`

Explanation

:. Area of `DeltaOAB=(1)/(2)|vec(OA)xxvec(OB)|`
`=(1)/(2)|(2hati-3hatj+2hatk)xx(2hatj+3hatj+hatk)|`
`=(1)/(2)|[hati,hatj,hatl],[2,-3,2],[2,3,1]|`
`=(1)/(2)|[hati(-3-6)-hatj(2-4)+hatk(6+6)]|`
`=(1)/(2)|-9i+2hatj+12hatk|`
:. Area of `DeltaOAB=(1)/(2)sqrt((81+4+144))=(1)/(2)sqrt229`