Show that the three lines with direction cosines are mutually perpendicular.

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

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

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector

Find the equation of the line in vector and in cartesian form that passes through the point with position vector and is in the direction

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 of a line is . Write its vector form.

Find the vector and the cartesian equations of the lines that passes through the origin and (5, –2, 3).

. Find the vector and the cartesian equations of the line that passes through the points (3, –2, –5), (3, –2, 6).

Find the angle between the following pairs of lines:

. Find the angle between the following pair of lines:

Find the values of p so that the lines are at right angles.

Show that the lines are perpendicular to each other.

Find the shortest distance between the lines

Find the shortest distance between the lines

Find the shortest distance between the lines whose vector equations are

Find the shortest distance between the lines whose vector equations are