If `veca+2vecb+3vecc=vec0 and veca xx vecb + vecb xx vecc + vecc xx veca =lambda(vecb xx vecc),` then what is the value of `lambda` ?

Options

A. `2`
B. `3`
C. `4`
D. `6`

Answer

D

Explanation

`vec(a)+2vec(b)+3vec(c)=vec(0) ...(1)`
`vec(a)xxvec(b)+vec(b)xxvec(c)+vec(c)xxvec(a)=lambda(vec(b)xxvec(c)) ...(2)`
`(1)xxvec(b)rArr vec(b)xxvec(a)+2vec(b)xxvec(b)+3vec(b)+3vec(b)xxvec(c)=0`
`rArr -vec(a)xxvec(b)+0+3vec(b)xxvec(c)=0`
`vec(a)xxvec(b)=3vec(b)xxvec(c) ...(3)`
`(1)xxvec(c)rArr vec(c)xxvec(a)+2vec(c)xxvec(b)+3vec(c)xxvec(c)=0`
`rArr vec(c)xxvec(a)-2vec(b)xxvec(c)+0=0`
`rArr vec(c)xxvec(a)=2vec(b)xxvec(c) ...(4)`
`:. (2)rArr vec(a)xxvec(b)+vec(b)xxvec(c)+vec(c)xxvec(a)=lambda ( vec(b)xxvec(c))`
`rArr 3 vec(b)xxvec(c)+vec(b)xxvec(c)+2(vec(b)xxvec(c))=lambda(vec(b)xxvec(c))` (from (3),(4))
`rArr 6(vec(b)xxvec(c))=lambda(vec(b)xxvec(c))`
`:. lambda=6`