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  • Created by: eleanor
  • Created on: 22-04-15 17:55
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  • Vectors
    • Cartesian Vectors
      • i= movement in x direction
        • j in y direction
          • k in z direction
      • magnitude of the vector = lentgh of it
        • =
      • direction of vectors in 2D
        • sketch the vector
          • we want the angle that the vector makes with the x axis  use socahtoa
      • distance between two points is the difference between each coordinate square then sqaurerooted
      • Parallel Vectors
        • parallel vectors have the same direction and are multiplies of each other
          • so 2i + 3j + 4k is parallel to 6i + 9j + 12k
      • Unit Vectors
        • these have a magnitude of 1
        • find the unit vector parallel
        • step one find the magnitude
        • step 2: divide by the magnitude to get the unit vector
    • Scalar Product : Dot product           a  b = x1x2 + y1y2 + z1z2
    • Straight Lines
      • r = p + Kq
        • position vector of a point on the line
        • a scalar (number)
        • Direction vector
      • method 1- given 2 points that lie on the line
        • find the vector equation of the line joining 2 vectors
          • 1. find the direction vector AB = b-a
          • 2. r = point A + K(direction vector)
      • method 2- given a point on the line and a parallel vector
        • if it passes through point A use that  as the point  and then use the direction vector that the line is parallel to
      • Method 3-
        • Given a point on the line and told that it is parallel to an axis
        • use point A that you are given that make the direction vector by putting a 1 in the coordinate of the axis
    • Perpendicular Lines: if a dot b = 0
      • a and b must be direction vectors for this to work
      • convert the lines into column vectors
      • find the scalar product using the direction vectors
    • Parallel lines: if a dot b = |a| dot |b|
    • angles between 2 straight lines
      • cos(x) = a.b/|a||b|
      • identify the direction vectors then find the magnitudes
      • find the scalar product  then sub into formula
    • finding if 2 line intersect
      • step 1: set the two equations of the line equal to each other then evaluate components separately
        • solve 2 of the equations simultaneously to find s and t then substitute them into the third equation and if they are equal they intersect
    • finding if a point lies on a line
      • equate the position vector of the point to the equation of the line
        • equate the i, j, k components separately to get 3 equations
          • solve each equation to find the unknown if they are all the same the cooridnate does lie o the line
    • finding the shortest distance from a point
      • find any lengths and angles needed in the triangle
        • then use socahtoa to find the missing side


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