Q. 15

# Find the vector equation of a line passing through the point (2, 3, 2) and parallel to the line Also, find the distance between these lines.HINT: The given line isThe required line isNow, find the distance between the parallel lines L1 and L2.

Given : point A ≡ (2, 3, 2)

Equation of line :

To Find : i) equation of line

ii) distance d

Formulae :

1. Equation of line :

Equation of line passing through point A (a1, a2, a3) and parallel to vector is given by

Where,

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,

As the required line is parallel to the line

Therefore, the vector parallel to the required line is

Given point A ≡ (2, 3, 2)

Therefore, equation of line passing through A and parallel to is

Now, to calculate distance between above line and given line,

Here,

= 7

Therefore, the shortest distance between the given lines is

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