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Statement-1: The point A(1, 0, 7) is the mirror image of the point B(1, 6, 3) in the line x/1 = (y - 1)/2 = (z - 2)/3.
Statement-2: The line x/1 = (y - 1)/2 = (z - 2)/3 bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).
- 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
Statement-1 is true because the coordinates of point A are indeed the mirror image of point B with respect to the given line, confirming their symmetrical relationship. Statement-2 is also true as the line bisects the segment joining A and B, but it does not serve as an explanation for the mirror image relationship established in 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.
Choose the correct option.
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