If the four points with position vectors `−2 hat i+ hat j+ hat k, hat i+ hat j + hat k, hat j – hat k` and `λ hat j+ hat k` are coplanar, then `λ=`

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`