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If the system of linear equations x+2ay...

If the system of linear equations `x+2ay +az =0,x+3by+bz =0 and x+4cy + cz =0` has a non-zero solution, then `a, b, c` are in

A

`A.P.`

B

`G.P.`

C

`H.P.`

D

satisfies `a+2b+3c=0`

Text Solution

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The correct Answer is:
C
`(c )` The system of linear equation has a non zero solution.
`Delta=|{:(1,2a,a),(1,3b,b),(1,4c,c):}|=0`
`:.(3bc-4bc)-(2ac-4ac)+(2ab-3ab)=0`
`:.bc+ab=2ac`
`:. (1)/(a)+(1)/(c )=(2)/(b)`
`impliesa,b,c` are in `H.P.`
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