Answer :

__Given__**:** Cartesian equations of lines

__To Find__**:** i) vector equations of given lines

ii) distance d

__Formulae__**:**

**1. Equation of line :**

Equation of line passing through point A (a_{1}, a_{2}, a_{3}) and having direction ratios (b_{1}, b_{2}, b_{3}) is

Where,

And

**2. Cross Product :**

If are two vectors

then,

**3. Dot Product :**

If are two vectors

then,

**4. Shortest distance between two parallel lines :**

The shortest distance between the parallel lines and

is given by,

__Answer__**:**

Given Cartesian equations of lines

Line L1 is passing through point (1, 2, -4) and has direction ratios (2, 3, 6)

Therefore, vector equation of line L1 is

And

Line L2 is passing through point (3, 3, -5) and has direction ratios (4, 6, 12)

Therefore, vector equation of line L2 is

Now, to calculate distance between the lines,

Here,

As , given lines are parallel to each other.

Therefore,

= 7

Therefore, the shortest distance between the given lines is

Rate this question :

Find the shortestMathematics - Board Papers

Show that the linMathematics - Board Papers

Find the shortestMathematics - Board Papers

Find the shortestMathematics - Board Papers