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If the plane 3x + y + 2z + 6 = 0 is para...

If the plane `3x + y + 2z + 6 = 0` is parallel to the line `(3x - 1)/(2b)=3-y=(z-1)/a`. then the value of `3a + 3b` is

A

`(1)/(2)`

B

`(3)/(2)`

C

3

D

4

Text Solution

Verified by Experts

The correct Answer is:
B
Given line can be rewritten as
`(x-(1)/(3))/((2b)/(3))=(y-3)/(-1)=(z-1)/(a)`
Given plane `3x+y+2z+6=0` is parallel to the above line, it means normal of the plane is perpendicular to the line.
`:." "(2b)/(3)*3+1*(-1)+2*a=0[becausea_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2)=0]`
`rArr" "2a+2b=1rArr3a+3b=(3)/(2)`
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