The shortest distance between the lines x-1-2-y-1-3-z-1-4 - x-1-3-y-4-z-5 is

The correct option is B 1/√(6)For line l_1, it passes through a⃗= i j k having d⃗_⃗1⃗=2i+3j+4k (direction) For line 2, it passes through b⃗= i havin ...

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Standard XII

Physics

Introduction

The shortest ...

Question

The shortest distance between the lines $\frac{x + 1}{2} = \frac{y + 1}{3} = \frac{z + 1}{4}; \frac{x + 1}{3} = \frac{y}{4} = \frac{z}{5}$ is

1

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\frac{1}{\sqrt{2}}

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\frac{1}{\sqrt{3}}

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\frac{1}{\sqrt{6}}

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Solution

The correct option is D $\frac{1}{\sqrt{6}}$
For line $l_{1}$ , it passes through
$\to a = - i - j - k$
having $_{1} = 2 i + 3 j + 4 k$ (direction)
For line 2, it passes through
$\to b = - i$
having $_{2} = 3 i + 4 j + 5 k$
Minimum distance between 2 times $= (\to b - \to a) . \frac{_{1} \times_{2}}{|_{1} \times_{2} |}$
$= \frac{1}{\sqrt{6}}$

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Similar questions

Q. Find the shortest distance between the lines

\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}

and

\frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}

Q. The shortest distance between the parallel lines:

\frac{x - 3}{4} = \frac{y - 1}{2} = \frac{z - 5}{- 3}

and

\frac{x - 1}{4} = \frac{y - 2}{2} = \frac{z - 3}{- 3}

Q. Find the shortest distance between lines:

\frac{x - 1}{1} = \frac{y - 2}{3} = \frac{z - 3}{2}

and

\frac{x - 4}{2} = \frac{y - 5}{3} = \frac{z - 6}{1}

Q. The shortest distance between the lines

\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}

and

\frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}

, is

Q. Find the shortest distance between two lines :

\frac{x - 1}{2} = \frac{y - 2}{3} = \frac{z - 3}{4}

and

\frac{x - 2}{3} = \frac{y - 4}{4} = \frac{z - 5}{5}

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The shortest distance between the lines x+12=y+13=z+14;x+13=y4=z5 is

The correct option is D 1√6For line l1, it passes through →a=−i−j−k having →d1=2i+3j+4k (direction) For line 2, it passes through →b=−i having →d2=3i+4j+5k Minimum distance between 2 times =(→b−→a).→d1×→d2|→d1×→d2| =1√6

The shortest distance between the lines $\frac{x + 1}{2} = \frac{y + 1}{3} = \frac{z + 1}{4}; \frac{x + 1}{3} = \frac{y}{4} = \frac{z}{5}$ is