The length of the perpendicular from (1,0,2) on the line 3 x + 1 = − 2 y − 2 = − 1 z + 1 is

The line passes through (-1, 2, -1) with direction (3, -2, -1). For w = ( 2 , − 2 , 3 ) , ∣ w ∣ 2 = 17 and w ⋅ ( 3 , − 2 , − 1 ) = 7 . The distance □ 2 is 17 − 14 49 = 2 27 , so the distance is 2 3 6 .

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Mathematics3D-Coordinate GeometryLine ( Equation etc.)Medium2 minQB

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The length of the perpendicular from (1,0,2) on the line $\frac{x + 1}{3} = \frac{y - 2}{- 2} = \frac{z + 1}{- 1}$ is

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The line passes through (-1, 2, -1) with direction (3, -2, -1). For $w = (2, - 2, 3)$ , $∣ w ∣^{2} = 17$ and $w \cdot (3, - 2, - 1) = 7$ . The distance $□^{2}$ is $17 - \frac{49}{14} = \frac{27}{2}$ , so the distance is $\frac{3 6}{2}$ .

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

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