EXERCISE 6.5

EXERCISE . . Find the parametric form of vector equation and Cartesian equations of a straight line passing through ( , , ) and is perpendicular to the straight lines ( s ( ) ) t i . Show that the lines ( ) ) s i ( ) ( ) are skew lines and hence find the shortest distance between them. . If the two lines m intersect at a point, find the value of m . . Show that the lines x −= and x −= intersect. Also find the point of intersection. . Show that the straight lines + = are skew and hence find the shortest distance between them. . Find the parametric form of vector equation of the straight line passing through ( , , ) parallel to the straight line ( t i and hence find the shortest distance between the lines. . Find the foot of the perpendicular drawn from the point ( , , ) to the line . Also, find the equation of the perpendicular.