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The system of linear equations x + y +...

The system of linear equations
`x + y + z =0`
`(2x)/(a)+(3y)/(b)+(4z)/c=0`
`x/a+y/b+z/c=0`
has non trivial solution then :

A

a + b + c = 0

B

a, b, c are in GP

C

`(1)/(a), (1)/(b), (1)/(c )` are in AP

D

a,b,c are in AP

Text Solution

Verified by Experts

The correct Answer is:
D
`|{:(1,1,1),((2)/(a),(3)/(b),(4)/(c )),((1)/(a),(1)/(b),(1)/(c )):} |`
`1((3)/(bc) - (4)/(bc)) - 1 ((2)/(ac) - (4)/(ac)) + 1 ((2)/(ab) - (3)/(ab)) = 0`
`- (1)/(bc) + (2)/(ac) - (1)/(ab) = 0` `implies` -a + 2b - c = 0 `implies` a,b,c are in AP
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