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) = (–1,2,1) and the required line is parallel to a given line which is not in the general form of the Cartesian equation because the coefficients of x,y,z in the Cartesian equation are 1, so the equation will reduce to the form 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 = 2λ, b = λ, c = –3λ
hence the equation of the required line is,
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