The vectors `x hati + (x+1)hatj + (x+2)hatk, (x+3)hati+ (x+4)hatj + (x+5)hatk and (x+6)hati + (x+7)hatj+ (x+8)hatk` are coplanar if x is equal to

Options

A. 1
B. -3
C. 4
D. 0

Answer

A, B, C, D

Explanation

` x hati + (x + 1) hatj + (x +2) hatk , ( x+3) hati + (x +4) hatj + ( x+5) hatk and ( x+6) hati + (x+7) hatj+ ( x+8) hatk` are coplanar. We have determinant of their coefficients
as `|{:(x,,x+1,,x+2),(x+3,,x+4,,x+5),(x+6,,x+7,,x+8):}|`
Applying `C_2 to C_2 - C_1 and C_3 to C_3-C_1`, we have
`|{:(x,,1,,2),(x+3,,1,,2),(x+6,,1,,2):}|=0`
Here , `x in R`.