Find the shortest distance between the lines

Question

Philoid · Accepted Answer

We know that

_{Shortest distance between the lines:}

and is

…(i)

The standard form of a pair of Cartesian lines is:

and

And the given equations are: and

_{Comparing the given equations with the standard form, we get}

_x₁ = -1, y₁ = -1, z₁ = -1; x₂ = 3, y₂ = 5, z₂ = 7

_a₁ = 7, b₁ = -6, c₁ = 1; a₂ = 1, b₂ = -2, c₂ = 1

_{Now, consider}

_⇒

⇒

Next, consider

⇒

_⇒ _{From (i), we have}

⇒