Chapter 11 – Three Dimensional Geometry

1. Write the direction cosines of the x-axis.

2. What is the condition for two lines to be perpendicular?

3. Write the symmetric form of a line in 3D.

4. How are direction cosines related?

5. What is the shortest distance between intersecting lines?

6. State the condition for two lines to be parallel.

1. Find the direction cosines of the line joining (1,2,3) and (3,5,7).

2. Find the angle between lines having direction ratios (1,2,2) and (2,1,2).

3. Determine whether two given direction-ratio sets represent perpendicular lines.

1. Find the equation of the line through (1,2,3) parallel to 2i−j+3k.

2. Find the angle between the lines with direction ratios (1,2,3) and (2,−1,1).

3. Find the distance of the point (1,2,3) from the plane x+2y+2z=9.

1. Derive the formula for the shortest distance between two skew lines represented in vector form. Explain the geometrical meaning of the scalar triple product appearing in the formula.