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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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