Find the shortest distance between the lines x-1-7-y-1-6-z-1-1 and x-3-1-y-5-2-z-7-1

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Byju's Answer

Standard XII

Mathematics

Conditions for a system of linear equations to have a unique solution

Find the shor...

Question

Find the shortest distance between the lines and

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Solution

The given lines are and

It is known that the shortest distance between the two lines, , is given by,

Comparing the given equations, we obtain

Substituting all the values in equation (1), we obtain

Since distance is always non-negative, the distance between the given lines is units.

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Similar questions

Find the shortest distance between the lines
$\frac{x + 1}{7} = \frac{y + 1}{- 6} = \frac{z + 1}{1} a n d \frac{x - 3}{1} = \frac{y - 5}{- 2} = \frac{z - 7}{1}$

Q. Find the shortest distance between the lines:

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

and

\frac{x + 3}{3} = \frac{y - 5}{2} = \frac{z - 7}{6}

Q. Find the shortest distance between lines:

\frac{x - 3}{1} = \frac{y - 5}{2} = \frac{z - 7}{1}

and

\frac{x + 1}{7} = \frac{y + 1}{- 6} = \frac{z + 1}{1}

Q. Find the shortest distance between lines

\frac{x + 1}{7} = \frac{y + 1}{- 6} = \frac{z + 1}{1}

and

\frac{x - 3}{1} = \frac{y - 5}{- 2} = \frac{z - 7}{1}

Q. The shortest distance between lines

\frac{x + 1}{7} = \frac{y + 1}{- 6} = \frac{z + 1}{1}

and

\frac{x - 3}{7} = \frac{y - 5}{- 6} = \frac{z - 7}{1}

approximately is

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Find the shortest distance between the lines and

The given lines are and It is known that the shortest distance between the two lines, , is given by, Comparing the given equations, we obtain Substituting all the values in equation (1), we obtain Since distance is always non-negative, the distance between the given lines is units.

The given lines are and

It is known that the shortest distance between the two lines, , is given by,

Comparing the given equations, we obtain

Substituting all the values in equation (1), we obtain

Since distance is always non-negative, the distance between the given lines is units.