Statement-1 : The point A(1, 0, 7) is the mirror image of the point B (1, 6, 3) in the line \(\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}\) Statement 2 : The line : \(\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}\) bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).

Engineering

Mathematics

Equation of Straight Line in 3D

Question

Statement-1 : The point A(1, 0, 7) is the mirror image of the point B (1, 6, 3) in the line \(\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}\)

Statement 2 : The line : \(\frac{x}{1} = \frac{{y - 1}}{2} = \frac{{z - 2}}{3}\) bisects the line segment joining A(1, 0, 7) and B(1, 6, 3).

Statement-1 is true, Statement-2 is false and Statement-2 is not the correct explanation of 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 and Statement-2 is the correct explanation of Statement-1.

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Mid- point of AB º M(1,3,5)

M lies on line

Direction ratios of AB is < 0, 6, – 4 >

Direction ratios of given line is < 1, 2, 3 >

As AB is perpendicular to line

\ 0.1 + 6.2 – 4.3 = 0

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