If the planes `x-c y-b z=0,c x=y+a z=0a n db x+a y-z=0` pass through a straight line, then find the value of `a^2+b^2+c^2+2a b cdot`

Options

A. `1-abc`
B. `abc-1`
C. `1-2abc`
D. `2abc-1`

Answer

C

Explanation

We have, `x-cy-bz=0`
`cx-y+az=0`
and `bx+ay-z=0`
Since, these planes are passing through a straight line
`therefore|(1,-c,-b),(c,-1,a),(b,a,-1)|=0`
`implies(1-a^(2))+c(-c-ab)-b(ac+b)=0`
`implies1-a^(2)-c^(2)-abc-abc-b^(2)=0`
`impliesa^(2)+b^(2)+c^(2)=1-2abc`