1. Lines in Space

2. z x y P Q Equation of a Line

3. z x y r0r0 d P Q

4. z x y r0r0 d r P Q Q’ Equation of a Line

5. z x y r0r0 d r P Q Q’ P(x 0,y 0,z 0 ) Q(x 1,y 1,z 1 ) Q’(x,y,z) d=d 1 i+d 2 j+d 3 k r 0 =x 0 i+y 0 j+z 0 k =(x 1 -x 0 )i+(y 1 -y 0 )j+(z 1 -z 0 )k Equation of a Line

6. z x y r0r0 d r P Q Q’ P(x 0,y 0,z 0 ) Q(x 1,y 1,z 1 ) Q’(x,y,z) Vector Parameterization d=d 1 i+d 2 j+d 3 k r 0 =x 0 i+y 0 j+z 0 k =(x 1 -x 0 )i+(y 1 -y 0 )j+(z 1 -z 0 )k Equation of a Line

7. z x y r0r0 d r P Q Q’ P(x 0,y 0,z 0 ) Q(x 1,y 1,z 1 ) Q’(x,y,z) Vector Parameterization d=d 1 i+d 2 j+d 3 k r 0 =x 0 i+y 0 j+z 0 k =(x 1 -x 0 )i+(y 1 -y 0 )j+(z 1 -z 0 )k Equation of a Line

8. z x y r0r0 d r P Q Q’ P(x 0,y 0,z 0 ) Q(x 1,y 1,z 1 ) Q’(x,y,z) Vector Parameterization d=d 1 i+d 2 j+d 3 k r 0 =x 0 i+y 0 j+z 0 k =(x 1 -x 0 )i+(y 1 -y 0 )j+(z 1 -z 0 )k Equation of a Line

9. z x y r0r0 d r P Q Q’ P(x 0,y 0,z 0 ) Q(x 1,y 1,z 1 ) Q’(x,y,z) Scalar Parametric Equations Vector Parameterization d=d 1 i+d 2 j+d 3 k r 0 =x 0 i+y 0 j+z 0 k =(x 1 -x 0 )i+(y 1 -y 0 )j+(z 1 -z 0 )k Equation of a Line

10. Representations of a Line

11. Examples

12. Direction Cosines

13. Example

16. Examples Find the equation of of the line through the origin and perpendicular to the plane pictured. Find the equation of the plane perpendicular to x(t)=4-2t, y(t)= -1+t, z(t)=3 z x y 3 5 4