Let `veca=hati-hatk, vecb=xhati+hatj+(1-x)hatk` and `vecc=yhati+xhatj+(1+x-y)hatk`, then `[veca vecb vecc]` depends on

Options

A. Only x
B. Only y
C. Both x and y
D. Neither x nor y

Answer

D

Explanation

Given vectors are
`a = hati - hatk , b = x hati + hatj + (1-x) hatk`
and `c = y hati + x hatj + (1+x-y) hatk`
Now, `[abc] = |{:(1,0,-1),(x,1,1-x),(y,x,1+x-y):}|`
On applying `C_(3) rarr C_(3) + C_(1)`, we get
`= |{:(1,0,0),(x,1,1),(y,x,1+x):}|`
Thus, [a,b,c] depends upon neither x nor y.