A quick summary of key ideas:

1. Collinearity of 3 points and the Ratio Theorem.

2. Definition of the scalar product,
i.e. a . b = |a| |b| cos \theta.

This definition is useful for finding length of projection of one vector onto another, angle between 2 vectors, angle between 2 lines, angle between 2 planes and angle between line and plane.

3. Definition of the magnitude of the vector product,
i.e. |a x b| = |a| |b| sin \theta.

This definition is useful for finding shortest distance between point and line as well as area of a triangle or parallelogram.

4. The normal vector c is parallel to a x b means that c is perpendicular to each of a and of b. This idea is extremely helpful for finding equation of a plane containing a line and is parallel to some vector. It is also useful to understand the line of intersection between two planes.

5. The relationship between two lines may be intersecting, parallel or skew.

6. The relationship between three planes may be intersecting at a point, intersecting at a line, parallel or non-intersecting at a point or line.

7. The relationship between a line and a plane may be intersecting, parallel or containment (i.e. line is on the plane).

8. Equation of a line may be expressed in vector, parametric or cartesian forms. Equation of a plane may be expressed in vector, scalar product or cartesian forms.

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