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Mathematics - 3D-Coordinate Geometry Question with Solution | TestHub

Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediumsingle choice

Three lines $y - z - 1 = 0 = x; z + x + 1 = 0 = y; x - z - 1 = 0 = y$ intersect the xy plane at A, B, C. Then the orthocentre of triangle ABC is

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Solution:

Intersection of $y - z - 1 = 0 = x$ with the xy plane ( $z = 0$ ) gives $A (0, 1, 0)$ . Similarly $B (- 1, 0, 0)$ and $C (1, 0, 0) . A B \cdot A C = (- 1, - 1, 0) \cdot (1, - 1, 0) = 0$ , so the angle at A is a right angle and the orthocentre is $A (0, 1, 0)$ .

Stream:JEESubject:MathematicsTopic:3D-Coordinate GeometrySubtopic:Line ( Equation etc.)

⏱ 2mℹ️ Source: QB

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