Question

Statement 1: For any three vectors `veca,vecb,vecc`
`[(vecaxxvecb,vecbxxvecc,veccxxveca)]=0`
Statement 2: If `vecp,vecq,vecr` are linear dependent vectors then they are coplanar.
A. 1
B. 2
C. 3
D. 4

Answer 1

Correct Answer - D
If `vecp,vecq,vecr` are linearly independent vectors, then there exist scalars `x,y,z` not all zero such that
`xvecp+yvecq+zvecr=vec0`
`impliesvecp=(-y/x)vecq+((-z)/x)vecr`
`impliesvecp,vecq,vecr` are coplanar.
So, statement 2 is true.
We know that `[(vecpxxvecb,vecbxxvecc,veccxxveca)]=[(veca,vecb,vecc)]!=0` unless `veca,vecb,vecc` are coplanar.
So, statement -2 is not true.