IIT-JEE 2007 · Paper 2 · Mathematics Q54

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MathematicsAssertion and reason+3 / -1Question 54 of 66

Consider the planes $3x-6y-2z=15$ and $2x+y-2z=5$ .

STATEMENT-1: The parametric equations of the line of intersection of the given planes are $x=3+14t$ , $y=1+2t$ , $z=15t$ .

because

STATEMENT-2: The vector $14\hat i+2\hat j+15\hat k$ is parallel to the line of intersection of given planes.

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1

Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1

Statement-1 is True, Statement-2 is False

Statement-1 is False, Statement-2 is True

Answer and worked solution

Official answer: D

Statement 2. The line of intersection is parallel to $\vec n_1\times\vec n_2$ :
$(3,-6,-2)\times(2,1,-2)=(12+2,\;-4+6,\;3+12)=(14,2,15).$
True.

Statement 1. At $t=0$ the point $(3,1,0)$ gives $3(3)-6(1)-2(0)=3\ne15$ : it is not on the first plane, so these are not the equations of the line. False.

(D)

Topics:Equation of a line in space Equation of a plane

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IIT-JEE 2007 · Paper 2, Mathematics question 54