# 6. Find the cartesian equation of the line which passes through the point (– 2, 4, – 5) and parallel to the line given by .

Given a line which passes through the point (– 2, 4, – 5) and is parallel to the line given by the ;

The direction ratios of the line,  are 3,5 and 6.

So, the required line is parallel to the above line.

Therefore we can take direction ratios of the required line as 3k, 5k, and 6k, where k is a non-zero constant.

And we know that the equation of line passing through the point  and with direction ratios a, b, c is written by: .

Therefore we have the equation of the required line:

or

The required line equation.

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