Discrete Mathematics - Vectors

Vectors

• Vectors and scalars, magnitude and direction of a vector

• Direction cosines and direction ratios of a vector

• Types of vectors (equal, unit, zero, parallel and collinear vectors), position vector of a point, negative of a vector, components of a vector, addition of vectors, multiplication of a vector by a scalar, position vector of a point dividing a line segment in a given ratio

• Definition, Geometrical Interpretation, properties and application of scalar (dot) product of vectors, vector (cross) product of vectors, scalar triple product of vectors

SUMMARY

1. The scalar components of a vector are its direction ratios, and represent its projections along the respective axes.

2. The vector sum of the three sides of a triangle taken in order is .

3. The vector sum of two coinitial vectors is given by the diagonal of the parallelogram whose adjacent sides are the given vectors.

4. The multiplication of a given vector by a scalar λ, changes the magnitude of the vector by the multiple |λ|, and keeps the direction same (or makes it opposite) according as the value of λ is positive (or negative).

5. The scalar product of two given vectors having angle θ between them.

6. The position vector of a point R dividing a line segment joining the points P and Q whose position vectors are a and b respectively, in the ratio m : n