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Statement-1: The point A(3, 1, 6) is the mirror image of the point B(1, 3, 4) in the plane x - y + z = 5.
Statement-2: The plane x - y + z = 5 bisects the line segment joining A(3, 1, 6) and B(1, 3, 4).
- 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.
- Statement -1 is true, Statement -2 is true; Statement -2 is a correct explanation for Statement -1.
Correct answer: Statement -1 is true, Statement -2 is true; Statement -2 is not a correct explanation for Statement -1.
Solution
Midpoint of A(3,1,6) and B(1,3,4) is (2,2,5), which satisfies x-y+z=5, and AB=(2,-2,2) is parallel to the normal (1,-1,1), so A is the mirror image of B (Statement-1 true). Statement-2 (the plane bisects AB) is also true, but bisection alone does not guarantee a mirror image (perpendicularity is also required), so Statement-2 is not a correct explanation of Statement-1.
Related JEE Main Maths questions
- Consider the following two statements:
Statement 1: If A, B and C are points with position vectors a = 2î + ĵ + k̂, b = 3î - ĵ + 3k̂ and c = î + 7ĵ - 5k̂, then the figure OABC forms a tetrahedron.
Statement 2: If the position vectors a, b and c of points A, B and C are non-coplanar, then OABC is a tetrahedron, where O denotes the origin.
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