Vectors





     Vectors is a study of a quantity which has both magnitude and direction. It is always denoted by a line segment with arrow head. The length of the line marks the magnitude and arrow head denotes the direction.

     Common representation of vectors is bold letter like V or bold letter with arrow mark above it  

      The direction is mostly expressed as counter clock wise rotation  about its 'tail' (that is the starting point ) from East. For Example a vector with direction of 50 degrees (50⁰) is a line that has been rotated 50 degrees in the counter clock wise direction from due East in the coordinate plane. The following diagram shows how to denote the direction.

        Magnitude is the scalar quantity and it denotes how much length the line or vector is. It is always mentioned by a number or a unit.   The magnitude of a vector is denoted by absolute signs around vector, ∣v∣; or just the letter without bold face like v.

Examples of vectors  are velocity, increase/decrease in temperature so on.

Note

  1. OP is not equal to PO. In magnitude both are equal but in direction they are opposite.
  2. Two vectors A and B are equal if only if they have the same magnitude and direction.
  3. A vector having the same magnitude as V but opposite direction is denoted by -V

                                                   Scalar

    Scalars are quantity that is described by numerical value that is magnitude. There is no direction described for scalar.

Examples for scalar is distance, time, speed and so on.

Note:  The measurement of temperature is a scalar quantity but measurement of increase/decrease in temperature is a vector quantity.

                                            Unit vectors

    Unit vectors are vectors of unit length used to denote the directions of the vector quantities in various coordinate system. 'i', 'j' and 'k' are used to represent unit vectors in x, y and z direction in Caretesian coordinate system.

      r= xî +yĵ+zk̂  is the position vector of a point in space with respect to the origin.  a





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