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Questions  

 The three planes 4y+6z=5,2x+3y+5z=5 and 6x+5y+9z=10

a
meet in a point
b
have a line in common
c
form a triangular prism
d
none of these

detailed solution

Correct option is B

Plane passing through the line of intersection of planes 4y+6z=5 and 2x+3y+5z=5 is  (4y+6z−5)+λ(2x+3y+5z−5)=0 or  2λx+(3λ+4)y+(5λ+6)z−5λ−5=0 Clearly, for λ=−3, we get the plane 6x+5y+9z=10 Hence, the given three planes have common line of intersection.

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