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Question

Find the Cartesian equation of the line which passes through the point (2,4,5) and parallel to the line given by x+33=y45=z+86

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Solution

It is given that the line passes through the point (2,4,5) and is parallel to x+33=y45=z+86 ....(1)
The direction ratios of the line (1) are 3,5 and 6.

The required line is parallel to equation (1).

Therefore, its direction ratios are 3k,5k and 6k, where k0.

It is known that the equation of the line through the point (x1,y1,z1) and with direction ratios, a,b,c is given by xx1a=yy1b=zz1c

Therefore, the equation of the required line is,

x+23k=y45k=z+56k

x+23=y45=z+56

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