Answer :

We are given with two lines.

…(i)

…(ii)

Take equation (i),

…(iii)

We know that,

Vector equation of a line passing through a point and parallel to a vector is , where λ ∈ ℝ.

Comparing it with equation (iii), we get

Now, take equation (ii),

…(iv)

Similarly from (iv),

So,

Shortest distance between two lines is given by

Solve .

Take 1^{st} row and 1^{st} column, multiply the first element of the row (a_{11}) with the difference of multiplication of opposite elements (a_{22} × a_{33} – a_{23} × a_{32}), excluding 1^{st} row and 1^{st} column.

Here,

Now take 1^{st} row and 2^{nd} column, multiply the second element of the row (a_{12}) with the difference of multiplication of opposite elements (a_{21} × a_{33} – a_{23} × a_{31}), excluding 1^{st} row and 2^{nd} column.

Here,

Similarly, take 1^{st} row and 3^{rd} column, multiply the third element of the row (a_{13}) with the difference of multiplication of opposite elements (a_{22} × a_{33} – a_{23} × a_{32}), excluding 1^{st} row and 3^{rd} column.

Here,

Further, simplifying it.

…(v)

And,

…(vi)

Now, solving .

…(vii)

Substituting values from (v), (vi) and (vii) in d, we get

⇒ d = 14

**Thus, the shortest distance between the given lines is 14 units.**

Rate this question :

Find the shortestMathematics - Board Papers

Show that the linMathematics - Board Papers

Find the shortestMathematics - Board Papers

Find the shortestMathematics - Board Papers