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

Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

MathematicsMediuminteger

Shortest distance between the z-axis and the line $x + y + 2 z - 3 = 0 = 2 x + 3 y + 4 z - 4$ is

Answer:

Solution:

Equation of any plane ; continuing the general plane is $x + y + 2 z - 3 + λ (2 x + 3 y + 4 z - 4) = 0$ .........(1)

if plane (1) is parallel to $z$ -axis $\Rightarrow λ = - \frac{1}{2}$

Therefore plane, parallel to z -axis is $y + 2 = 0$

Now, shortest distance between any point on z-axis ( $0, 0, 0$ ) (say) from plane ( 2 ) is 2

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

⏱ 2mℹ️ Source: QB

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