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The vectors x hati + (x+1)hatj + (x+2)ha...

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

A

1

B

`-3`

C

`4`

D

0

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
`xhati+(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 coefficient 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`, hence, `x in R`.
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