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 is The required line is Now, 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    Rate this question :

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