LearnPick Navigation
Close

Cartesian Componants

Published in: Mathematics
231 views
  • Arman R

    • Rajkot
    • 4 Years of Experience
    • Qualification:
    • Teaches: Mathematics, Algebra
  • Contact this tutor

A PPT on Cartesian components. 

  • 1
    CARTESIAN COMPONENTS OF VECTORS
  • 2
    Two-dimensional Coordinate frames P(x.y) The diagram shows a two-dimensional coordinate frame. Any point P in the plane of the figure can be defined in terms of its x and y coordinates.
  • 3
    Y (All these vectors are multiples of i.) A unit vector pointing in the positive direction of the x- axis is denoted by i. Any vector in the direction of the x-axis will be a multiple of i. A vector of length I in the direction of the x-axis can be written li.
  • 4
    Y (All these vectors are multiples of j.) 25 4j A unit vector pointing in the positive direction of the y-axis is denoted by j. Any vector in the direction of the y-axis will be a multiple of j. A vector of length I in the direction of the y-axis can be written Ij.
  • 5
    Key Point i represents a unit vector in the direction of the positive x-axis. j represents a unit vector in the direction of the positive y-axis.
  • 6
    Example Draw the vectors 51 and 4j. Use your diagram and the triangle law of addition to add these two vectors together.
  • 7
    Any vector in the xy plane can be expressed in the form The numbers a and b are called the components of in the x and y directions. 24 ai
  • 8
    Example a) b) c) d) y Draw an xy plane and show the vectors 2 = 21 + 3j, and q = 51 + j. Express 2 and q using column vector notation. Show the sump + q. Express the resultant 2 + q in terms of i and j. 7 4j
  • 9
    Example If a = 9i + 7j and b = 8i +3j, find:
  • 10
    Key Point The position vector of P with coordinates (a, b) is: = OP = ai + bj P(a.b)
  • 11
    Example State the position vectors of the points with coordinates: a) b) c) d) S(8, —4)
  • 12
    Example Sketch the position vectors: y
  • 13
    The modulus of any vector r is equal to its length. As we have noted earlier the modulus of r is usually denoted by Irl. When r = ai + bj the modulus can be obtained using Pythagoras' theorem. If r is the position vector of point P then the modulus is clearly the distance of P from the origin.
  • 14
    Key Point if r = ai + bj then Ir
  • 15
    Example Point A has coordinates (3, 5). Point B has coordinates (7, 8). a) Depict these points on a diagram. b) State the position vectors of A and B. c) Find an expression for AB. d) Find IABI.
  • 16
    Thi www.worldofteaching.com http://www.worldofteachinq.com is home to over a thousand powerpoints submitted by teachers. This is a completely free site and requires no registration. Please visit and I hope it will help in your teaching.

Discussion

Copyright Infringement: All the contents displayed here are being uploaded by our members. If an user uploaded your copyrighted material to LearnPick without your permission, please submit a Takedown Request for removal.

Need a Tutor or Coaching Class?

Post an enquiry and get instant responses from qualified and experienced tutors.

Post Requirement

Related PPTs

Query submitted.

Thank you!

Drop Us a Query:

Drop Us a Query