8. Find the vector and the cartesian equations of the lines that passes through the origin and (5, – 2, 3).
GIven that the line is passing through the and
Thus the required line passes through the origin.
its position vector is given by,
So, the direction ratios of the line through and are,
The line is parallel to the vector given by the equation,
Therefore the equation of the line passing through the point with position vector and parallel to is given by;
Now, the equation of the line through the point and the direction ratios a, b, c is given by;
Therefore the equation of the required line in the Cartesian form will be;
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