Discrete Mathematics - Vectors

IIT-JEE Main & Advanced | BITSAT | SAT | MSAT | MCAT | State Board | CBSE | ICSE | IGCSE

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Description

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

What You Will Learn!

  • Introduction
  • Some Basic Concepts
  • Types of Vectors
  • Addition of Vectors
  • Multiplication of a Vector by a Scalar
  • Product of Two Vectors

Who Should Attend!

  • Complete Mathematics for Engineering Entrance Exam Preparation. ( IIT-JEE Main | Advanced | BITSAT | SAT | etc.)
  • Those preparing for board and competitive exams State Board, CBSE, ICSE , IGCSE, MHT-CET & NEET
  • Courses are suitable for 160 countries from Europe, America, Middle East, Asia, Africa and APAC. Notably England, Germany, France, Sweden, Ireland, Scotland, USA, Canada, UAE, Saudi, Qatar, Kuwait, Malaysia, Indonesia, Myanmar, Newzealand, Australia, South Africa, South Korea, Nigeria, Nepal, Sri Lanka, etc