Q. 125.0( 1 Vote )

# Find the equation of the line passing through the point (1, 2, –4) and parallel to the line

The Cartesian equation of a line passing through a point (x1, y1, z1) and having directional ratios proportional to a,b,c is given by,

Now the point (x1, y1, z1) = (1,2,–4) and the required line is parallel to a given line , now as we know that if two lines are parallel and direction ratios of one line are a,b,c then the direction ratios of other lines will be ka,kb,kc where k is a constant and which gets cancelled when we put these direction ratios in the equation of the required line.

So the direction ratios of the required line are ;

a = 4λ, b = 2λ, c = 3λ

hence the equation of the required line is,

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