This cheat sheet covers the high school math concept – Vector Geometry.
A vector is an object that has both a magnitude and a direction. Geometrically, we can picture a vector as a directed line segment – which is simply a segment with an arrow at one of its end points.
The arrow end is called the head and the other end is called the tail of the vector. We define the magnitude of this vector as the length of this segment. The direction of the vector is from its tail to its head.
Solution of geometrical problems is one of the most important applications of vectors. Many problems, which are otherwise quite difficult to solve using pure geometry (or even algebra), can be easily solved if vectors are used. Apart from that, vectors also find application in solving a lot of problems in physics.
A good knowledge of vector algebra is a must to understand and solve problems related to vector geometry. A cheat sheet on Vector Algebra is also available on this website.
The formulas and equations derived in this cheat sheet are closely linked to those in 3D analytical / coordinate geometry. A cheat sheet on 3D Geometry is also available on this website.
This one page PDF covers summarised theory and the most important formulas related to the concept. Keep it handy while you’re revising the concept, especially before an exam.
The topics included in this cheat sheet are:
- Equation of a line
- Angle between two lines
- Distance of a point from a line
- Distance between parallel lines
- Shortest distance between skew lines
- Equation of the angle bisectors of two lines
- Equations of a plane
- Angle between two planes
- Angle between a line and a plane
- Distance of a point from a plane
- Distance between parallel planes
- Family of planes
- Equation of the angle bisectors of two planes
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