The two lines `vecr=veca+veclamda(vecbxxvecc) and vecr=vecb+mu(veccxxveca)` intersect at a point where `veclamda and mu` are scalars then (A) `veca,vecb,vecc` are non coplanar (B) `|veca|=|vecb|=|vecc|` (C) `veca.vecc=vecb.vecc` (D) `lamda(vecbxxecc)+mu(veccxxveca)=vecc`

Options

A. `vecaxxvecc=vecbxxvecc`
B. `veca.vecc=vecb.vecc`
C. `vecbxxveca=veccxxveca`
D. none of these

Answer

b

Explanation

The lines `vecr= veca+lamda (vecbxxvecc) and vecr= vecb+mu (veccxxveca)` pass through points `veca and vecb`, respectively.
Therefore, they intersect if `veca-vecb, vecbxxvecc and vecc xx veca` are coplanar and so
`" "(veca-vecb)*{(vecbxxvecc)xx(veccxxveca)}=0`
or `" "(veca-vecb)*([vecbveccveca]vecc-[vecbveccvecc]veca)=0`
or `" "((veca-vecb)*vecc)[vecbveccveca]=0`
or `" "veca*vecc-vecb*vecc=0 or veca*vecc= vecb*vecc`