## Monday, November 3, 2008

### Ch. 31. THREE DIMENSIONAL GEOMETRY - Revision Facilitator

Relevant Sections in the Chapter

31.1 Coordinates of a point in space

31.2 Signs of Coordinates of a Point in Various Quadrants

31.3 Distance formula

31.4 Section formulas

31.5 Direction cosines and direction ratios
31.6 Angle between two vectors in terms of their directions cosines and direction ratios
31.7 Straight line in space
31.8 Angle between two lines
31.9 Intersection of two lines
31.10 Perpendiculars distance of a point from a line
31.11 Reflection or image of a point in a straight line

31.12 Shortest distance between two straight lines
31.13 Plane - Definition and Equation
31.14 Equation of plane passing through a given point

31.15 Intercept form of plane

31.16 Vector equation of a plane passing through a given point and normal to a given vector

31.17
a. Equation of a plane in normal form - Vector Form
b. Equation of a plane in normal form

31.19 Equation of a Plane Passing through a Given Point and Parallel to two Given Vectors

31.20 Equation of a Plane Parallel to a Given Plane

31.21 Equation of a Plane Passing through the Intersection of Two planes
31.22 Distance of a point from plane
31.24 Line and a plane
31.25 Angle between a line and plane
31.26 Intersection of a line and a plane
31.27 Condition of coplanarity of two line and equation of the plane containing them
31.28 Image of a point in a plane

Study Plan

Day 1

31.1 Coordinates of a point in space

31.2 Signs of Coordinates of a Point in Various Quadrants

31.3 Distance formula

31.4 Section formulas

Day 2

31.5 Direction cosines and direction ratios

Day 3

31.6 Angle between two vectors in terms of their directions cosines and direction ratios
31.7 Straight line in space

Day 4

31.8 Angle between two lines
31.9 Intersection of two lines
31.10 Perpendiculars distance of a point from a line

Day 5

31.11 Reflection or image of a point in a straight line

31.12 Shortest distance between two straight lines

Day 6

31.13 Plane - Definition and Equation
31.14 Equation of plane passing through a given point

31.15 Intercept form of plane

Day 7

31.16 Vector equation of a plane passing through a given point and normal to a given vector

31.17 Equation of a plane in normal form
31.18 Angle between two planes

Day 8

31.19 Equation of a Plane Passing through a Given Point and Parallel to two Given Vectors

31.20 Equation of a Plane Parallel to a Given Plane

31.21 Equation of a Plane Passing through the Intersection of Two planes
31.22 Distance of a point from plane

Day 9

31.23 Equations of planes bisecting the angles between two given planes
31.24 Line and a plane
31.25 Angle between a line and plane

Day 10

31.26 Intersection of a line and a plane
31.27 Condition of coplanarity of two line and equation of the plane containing them
31.28 Image of a point in a plane

Day 11

Illustrative Objective Type Examples 1 to 18 (Ignore what are not in the sections covered by you)

Day 12

Objective Type Exercise 1 to 20

Day 13
O.T.E.: 21 to 40

Day 14
O.T.E.: 41 to 60

Day 15
O.T.E.: 61 to 80

Revision Period

Day 16
Concept revision

Day 17
concept revision

Day 18 to 30
Test paper problems

Try to recollect and see how many you remember. I shall create the material related to them and link them over a period of time.

31.1 Coordinates of a point in space

31.2 Signs of Coordinates of a Point in Various Quadrants

31.3 Distance formula

31.4 Section formulas

Internal division

External division

31.5 Direction cosines and direction ratios

Direction cosines

Some theorems/results on direction cosines

Direction ratios

Some theorems/results on direction cosines and direction ratios

Direction cosines and direction ratios of a vector given inters of unit vectors

Direction ratios of the line joining two given points

Direction cosines of parallel vectors

Projections of vector on the coordinate axes

Direction cosines and direction ratios of a line

31.6 Angle between two vectors in terms of their directions cosines and direction ratios

31.7 Straight line in space
31.8 Angle between two lines
31.9 Intersection of two lines
31.10 Perpendiculars distance of a point from a line
31.11 Reflection or image of a point in a straight line

31.12 Shortest distance between two straight lines
Shortest distance between two skew lines - Vector Form
Shortest distance between two skew lines – Cartesian Form
Shortest distance between two parallel lines

31.13 Plane - Definition and Equation

31.14 Equation of plane passing through a given point

31.15 Intercept form of plane

31.16 Vector equation of a plane passing through a given point and normal to a given vector
Vector Form
Cartesian Form

31.17
a. Equation of a plane in normal form - Vector Form
b. Equation of a plane in normal form

31.19 Equation of a Plane Passing through a Given Point and Parallel to two Given Vectors

31.20 Equation of a Plane Parallel to a Given Plane

31.21 Equation of a Plane Passing through the Intersection of Two planes

31.22 Distance of a point from plane
31.24 Line and a plane
31.25 Angle between a line and plane
31.26 Intersection of a line and a plane
31.27 Condition of coplanarity of two line and equation of the plane containing them
31.28 Image of a point in a plane