Shortest distance between the lines x-11-y-11-z-11 and x-21-y-31-z-41 is equal to

The given lines are parallel. From the figure, we get BC=(2 1)1√(3)+(3 1)1√(3)+(4 1)1√(3) =1+2+3√(3)=2√(3) AB=√(1+4+9)=√(14) Shortest distance = AC=√(14 12)=√( ...

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Byju's Answer

Standard XII

Mathematics

Condition for Two Lines to Be Perpendicular

Shortest dist...

Question

Shortest distance between the lines $\frac{x - 1}{1} = \frac{y - 1}{1} = \frac{z - 1}{1}$ and $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{1}$ is equal to

\sqrt{14}

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\sqrt{7}

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\sqrt{2}

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\sqrt{3}

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Solution

The correct option is C $\sqrt{2}$
The given lines are parallel.

From the figure, we get
$B C = \frac{(2 - 1) 1}{\sqrt{3}} + \frac{(3 - 1) 1}{\sqrt{3}} + \frac{(4 - 1) 1}{\sqrt{3}}$
$= \frac{1 + 2 + 3}{\sqrt{3}} = 2 \sqrt{3}$
$A B = \sqrt{1 + 4 + 9} = \sqrt{14}$
Shortest distance = $A C = \sqrt{14 - 12} = \sqrt{2}$

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Similar questions

Q. Find the shortest distance between the lines

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

and

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

Q. Find the shortest distance between the lines

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

and

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

Q. 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}

Q. Find the shortest distance between lines:

\frac{x + 1}{- 10} = \frac{y + 3}{- 1} = \frac{z - 4}{1}

and

\frac{x + 10}{- 1} = \frac{y + 1}{- 3} = \frac{z - 1}{4}

Q. The shortest distance between the skew lines

\frac{x - 3}{- 1} = \frac{y - 4}{2} = \frac{z + 2}{1}, \frac{x - 1}{1} = \frac{y + 7}{3} = \frac{z + 2}{2}

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Condition for Two Lines to Be Perpendicular

Standard XII Mathematics

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Shortest distance between the lines x−11=y−11=z−11 and x−21=y−31=z−41 is equal to

The correct option is C √2The given lines are parallel. From the figure, we get BC=(2−1)1√3+(3−1)1√3+(4−1)1√3 =1+2+3√3=2√3 AB=√1+4+9=√14 Shortest distance = AC=√14−12=√2

Shortest distance between the lines $\frac{x - 1}{1} = \frac{y - 1}{1} = \frac{z - 1}{1}$ and $\frac{x - 2}{1} = \frac{y - 3}{1} = \frac{z - 4}{1}$ is equal to