# The Application of Vectors

This word document gives methods to work out angles, intersections and distances between lines, planes and points. Diagrams are included in each case.

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## Pages in this set

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The Application of Vectors
Items Angle between Distance between Intersection of
Plane and plane 1. 2. 3.
Plane and line 4. 5. 6.
Plane and point 7. 8. 9.
Line and point 10. 11. 12.
Line and line 13. 14. 15.
Point and point 16. 17. 18.

The basics…

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The position vector of a point in Cartesian space is the fixed vector from the origin to that
point. Hence if A is the point in Cartesian space with coordinates (1, 3, 6) , then its position

^ + 3^
vector OA = i ^.
j + 6 k…

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3. Intersection of two planes

4. Angle between a plane and a line

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5. Distance between a plane and a parallel line

6. Intersection of a plane and a line

7. The angle between a point and a plane

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8. The distance between a plane and a point

9. The intersection of a point and a plane

10. The angle between a line and a point

11. The distance between a line and a point

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12. The intersection of a line and a point

13. The angle between a line and a line

14. The perpendicular distance between two skew lines

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15. The intersection of two non-parallel lines

16. The angle between two points

17. The distance between two points

18. The intersection of two points

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