Let `veca =veci -veck, vecb = xveci+ vecj + (1-x)veck and vecc =y veci +xvecj + (1+x -y)veck`. Then `veca, vecb and vecc` are non-coplanar for

Options

A. some values of x
B. some values of y
C. no values of x and y
D. for all values of x and y

Answer

D

Explanation

`veca =hati -hatk `
`" " vecb = xhati +hatj + (1-x)hatk`
`" " vecc =yhati + xhatj+ (1+x-y)hatk`
`" "=|{:(1,,0,,-1),(x,,1,,1-x),(y,,x,,1+x-y):}|`
`" " = 1+x-y-x^(2)+y-x+x^(2)`
`= 1`