If `a( vecalphaxx vecbeta)+b( vecbetaxx vecgamma)+c( vecgammaxx vecalpha)=0` and at least one of `a ,ba n dc` is nonzero, then vectors ` vecalpha, vecbetaa n d vecgamma` are a. parallel b. coplanar c. mutually perpendicular d. none of these

Options

A. parallel
B. coplanar
C. mutually perpendicular
D. none of these

Answer

b

Explanation

Taking dot product of `a (vecalpha xx vecbeta) + b(vecbeta xx vecgamma) + c(vecgamma xx vecalpha) = 0 " with " vecgamma , vecalpha and vec beta` respectively.
we have
` a [vecalpha vecbeta vecgamma] =0`
`b [ vecalpha vecbeta vecgamma] =0`
`c[vecalpha vecbeta vecgamma] =0`
since at least one of a,b and c `ne 0`. we have
` [vecalpha vecbeta vecgamma ]= 0`
Hence `vecalpha, vecgamma , and vecgamma ` are coplanar.