Q4 of 136 Page 28

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

The Cartesian equation or the symmetrical form of equation is the one which is of the form

Where (x1,y1,z1) is the point through which the line passes and a,b,c are the directional ratios of the line or the directional ratios of the line are proportional to them.


The Cartesian equation of a line passing through the point (–2,4,–5) and parallel to the line


is .


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2

Show that the line through the points (1, –1, 2) and (3, 4, –2) is perpendicular to the through the point (0, 3, 2) and (3, 5, 6).

 3

Show that the line through the points (4, 7, 8) and (2, 3, 4) is parallel to the line through the points (–1, –2, 1) and (1, 2, 5).

 5

Show that the lines and are perpendicular to each other.

 6

that the line joining the origin to the point (2, 1, 1) is perpendicular to the line determined by the points (3,5,–1) and (4, 3, –1).