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
\(\vec r=\bar a_1+\lambda \bar{b}\)
Where,
4. Shortest distance between two parallel lines :
The shortest distance between the parallel lines \(\vec r=\bar a_1+\lambda \bar{b}\) and
\(\vec r=\bar a_2+\lambda \bar {b}\) is given by,
As the required line is parallel to the line
Therefore, the vector parallel to the required line is
Therefore, equation of line passing through A and parallel to \(\vec b\) is
Now, to calculate distance between above line and given line,
Therefore, the shortest distance between the given lines is