Specialist Maths Vectors and Geometry Week 4

Lines in Space Vector Equation Parametric Equations Cartesian Equation

Example 21 (Ex 4I)

Solution 21

Example 22 (Ex 4I)

Solution 22

Example 23 (Ex 4I)

Solution 23

Example 24 (Ex 4I)

Solution 24

Example 25 (Ex 4I)

Solution 25

Shortest distance from a point to a line

Example 26 (Ex 4I)

Solution 26

Parallel Lines are always in the same plane and don’t intersect l1l1 l2l2 Angle between parallel lines is zero

Intersecting lines will always be on the same plane θ l1l1 l2l2 To prove lines are in the same plane you show either that they Intersect or they are parallel. Angle between l 1 and l 2 is θ

Skew Lines are lines that are not parallel but do not meet. They lie in non parallel planes. Line 1 Line 2 Non parallel planes Skew Lines

Example 27 (Ex 4I)

Solution 27

Example 28 (Ex 4I)

Solution 28

Example 29 (Ex 4I)

Solution 29

Acute Angle between Lines A B u v Line 1 Line 2 Line 1´ P θ

Example 30 (Ex 4I)

Solution 30

Shortest Distance between Skew Lines A B u v Line 1 Line 2 P θ

Example 31 (Ex 4I)

Solution 31

This Week Text book pages 156 to 154. Exercise 4I Questions: 1 – 15.