Q. 165.0( 2 Votes )

# Write the vector

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 (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 parallel lines :

The shortest distance between the parallel lines and is given by, 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 :

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