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Mathematics - 3D Coordinate Geometry Question with Solution | TestHub

Mathematics3D Coordinate GeometryCoplanarity of two linesMedium2 minQB

MathematicsMediumsingle choice

The points $A (2 - x, 2, 2), B (2, 2 - y, 2), C (2, 2, 2 - z)$ and $D (1, 1, 1)$ are coplanar, then the locus of $P (x, y, z)$ is

Options:

Answer:

Solution:

$A B = x \hat{i} - y \hat{j}, A C = x \hat{i} - z \hat{k}, A D = (x - 1) \hat{i} - \hat{j} - \hat{k}$ . Coplanarity gives $x x x - 1 - y 0 - 1 0 - z - 1 = 0$

, which expands to

x yz = x y + yz + z x

, i.e.

\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1

Stream:JEESubject:MathematicsTopic:3D Coordinate GeometrySubtopic:Coplanarity of two lines

⏱ 2mℹ️ Source: QB

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