Q. 6

# Show that the lin

Given : Cartesian equations of lines  To Find : distance d

Formulae :

1. Equation of line :

Equation of line passing through point A (a1, a2, a3) and having direction ratios (b1, b2, b3) is Where, And 2. Cross Product :

If are two vectors  then, 3. Dot Product :

If are two vectors  then, 4. Shortest distance between two lines :

The shortest distance between the skew lines and is given by, Given Cartesian equations of lines Line L1 is passing through point (1, -1, 1) and has direction ratios (3, 2, 5)

Therefore, vector equation of line L1 is And Line L2 is passing through point (2, 1, -1) and has direction ratios (2, 3, -2)

Therefore, vector equation of line L2 is Now, to calculate distance between the lines,  Here,    Therefore,        Now,  = - 19 + 32 – 10

= 3

Therefore, the shortest distance between the given lines is   As d ≠ 0

Hence, given lines do not intersect each other.

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