Parametric and general equation of a geometrical object O EQUATION INPUT t OUTPUT EQUATION INPUT OUTPUT (x, y, z)

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Presentation transcript:

Parametric and general equation of a geometrical object O EQUATION INPUT t OUTPUT EQUATION INPUT OUTPUT (x, y, z)

System of co-ordinates in E 2 b1b1 b2b2 x y a1a1 a2a2 points vector s

System of co-ordinates in E 3 y z points vector s x

Parametric equations of a straight line A X in E 2 in E 3

Parametric equations of a plane A X

General equation of a straight line in E 2 If a straight line is given by two points then its general equation can be expressed as

General equation of a plane in E 3 If a plane is given by three points then its general equation can be expressed as

General equations of a straight line in E 3 No single general equation for a straight line in E 3 exists. It has to be replaced by general equations of the two planes that intersect in that straight line.

Given a general equation of a straight line how to determine a vector u parallel to and a vector v perpendicular to that straight line ?

Given a general equation of a plane how to determine a vector u perpendicular to that plane ?

Finding the coordinates of a vector u parallel to the straight line given by two general equations of planes

Angle between two straight lines

Angle between a plane and a straight line

Angle between two planes

The distance of a point from a straight line or a plane d d

Special type equation of a straight line (1) q negative positive x y

Special type equation of a straight line (2) x y a b

Special type equation of a plane y x z O A B C a b c

Canonical equations of a straight line in E 3

Bundle of straight lines l1l1 l2l2 l

Bundle of planes

Bunch of planes P A B C

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