Q. 215.0( 1 Vote )

# Find the shortest

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 .  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 1st row and 1st column, multiply the first element of the row (a11) with the difference of multiplication of opposite elements (a22 × a33 – a23 × a32), excluding 1st row and 1st column. Here, Now take 1st row and 2nd column, multiply the second element of the row (a12) with the difference of multiplication of opposite elements (a21 × a33 – a23 × a31), excluding 1st row and 2nd column. Here, Similarly, take 1st row and 3rd column, multiply the third element of the row (a13) with the difference of multiplication of opposite elements (a22 × a33 – a23 × a32), excluding 1st row and 3rd 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 :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Find the shortestMathematics - Board Papers

Show that the linMathematics - Board Papers

Find the shortestMathematics - Board Papers

Find the shortestMathematics - Board Papers