Match the entry in colum-I with the entry in column-II

Explanation

`A rarr (P), Brarr(s), Crarr(r), Drarr(q)`
(A) The equation of a plane passing through the point with position vector `veca` and parallel to vectors
`vecb` & `vecc` can be put in the form

`(vecr-veca)cdot(vecbxxvecc)=0` as the vectors `vecr-veca, vecb `&` vecc` are coplanar.
`rArr[vecr vecb vecc]=[veca vecb vecc]`
Also `vecr -veca,vecb, vecc` being coplanar, `vecr -a` can be expressed as a linear combination of `vecb` and
`vecc`, that is `vecr -veca= mvecb+nvecc`
giving `vecr = veca+ mvecb+nvecc`,
(B) The equation of the plane passing through `veca and vecb` and parallel to `vecc` can be put in the form
`[vecr -veca" "vecr-vecb " "vecc]=0` as the vectors `vecr-veca, vecr-vecband vecc` are coplanar.
(C) The equation of the plane passing through three points `veca, vecb & vecc (vecr-veca)`.
`{(vecb-veca)xx(vecc-veca)}=0` as `vec(AP), vec(AB)and vec(AC)` are coplanar.
(D) The equation of a line passing through the point `veca and hati` Parallel to `vecb-vecc` is given by
`vecr=veca+lambda (vecb-vecc).`