i. If `veca, vecb and vecc` are non-coplanar vectors, prove that vectors `3veca-7vecb-4vecc, 3veca-2vecb+vecc and veca+vecb+2vecc` are coplanar.
ii. If the vectors `2hati-hatj+hatk, hati+2hath-3hatk and 3hati+ahatj + 5hatk` are coplanar, the prove that `a=4`.

Explanation

i. If the given vectors are coplanar, then we should be able to express one of them as a linear combination of the other two.
Let us assume that `3veca-7vecb-4vecc=x(3veca-2vecb+vecc)+y(veca+vecb+2vecc),`
where `x and y` are scalars. Since `veca, vecb and vecc` are non-coplanar, equating the coefficients of `veca, vecb and vecc`, we get
`" "3x+y=3, -2x+y=-7, x+2y=-4`