Ques. -12

Geometry Level 4

Consider the intersection of two planes P 1 P_1 and P 2 P_2 is P 1 + λ P 2 = 0 P_1+\lambda P_2=0 .

Statement -1: The plane 5 x + 2 z 8 = 0 5x+2z-8=0 contains the line ( 2 x y + z 3 = 0 a n d 3 x + y + z = 5 ) \left( 2x-y+z-3=0 \ and \ 3x+y+z=5 \right) and is perpendicular to 2 x y 5 z 3 = 0 2x-y-5z-3=0 .

Statement-2: The plane 3 x + y + z = 5 3x+y+z=5 meets the line x 1 = y + 1 = z 1 x-1=y+1=z-1 at the point ( 1 , 1 , 1 ) (1,1,1) .

Which of the following options is true ?

a). Statement-1 is true, Statement-2 is true. And statement-2 is a correct explanation of statement-1.

b). Statement-1 is true, Statement-2 is true. But Statement-2 is not correct explanation of statement-1.

c). Statement-1 is true, Statement-2 is false.

d). Statement-1 is false, Statement-2 is true.


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d) b) c) a)

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1 solution

Prakhar Gupta
Mar 13, 2015

Clearly statement 2 is false as the point ( 1 , 1 , 1 ) (1,1,1) is not lying on the given line. This makes option c to be the correct option.

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