Introduction to vectors

Introduction to vectors

The notion of vectors can be easily found in our daily surroundings – from airplane navigation to trajectories of balls during a sports game, to movements of a character you maneuver in your video games. In this section, we will learn about the graphical, and mathematical representation of a vector, as well as how to distinguish the differences between a scalar quantity and a vector quantity.

Lessons

Vector Quantity: a quantity having (positive) magnitude and (one) direction
Scalar Quantity: a quantity having only magnitude but not direction
Two – Dimensional Vectors:

Introduction to vectors
  • 1.

  • 2.
    Which of the following is/are a vector?
    i)
    5050 miles per hour north
    ii)
    40km/s2\sqrt{40 } km/s^2
    iii)
    43.1C -43.1^{\circ} C
    iv) 5641ft35641\; ft^3
    v)
    3232 Newton at 9898^{\circ} west of north

  • 3.
    For the following vectors, express them in component form, matrix form, and rectangular form
    express vectors in component form, matrix form, and rectangular form

    a)
    p \vec{p}

    b)
    q \vec{q}

    c)
    v \vec{v}

    d)
    w \vec{w}


  • 4.
    For the following vectors, express them in component form, matrix form, and rectangular form
    vectors in various forms

    a)
    v \vec{v}

    b)
    w \vec{w}

    c)
    r \vec{r}