If `veca=hati-2hatj+3hatk, vecb=2hati+3hatj-hatk` and `vecc=rhati+hatj+(2r-1)hatk` are three vectors such that `vecc` is parallel to the plane of `veca` and `vecb` then`r` is equal to,

Options

A. `1`
B. `0`
C. `2`
D. `-1`

Answer

B

Explanation

It is given `vecc` is parallel to the plane of `veca` and `vecb`
`:.vecc_|_vecaxxvecb`
`impliesvecc(vecaxxvecb)=0implies[(veca, vecb, vecc)]=0`
`implies|(1,-2,3),(2,3,-1),(4,1,2r-1)|=0`
`implies(6r-2)+2(5r-2)+(6-9r)=0implies7r=0impliesr=0`.