C4 Vectors Summery

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  • Created by: Tassillow
  • Created on: 28-05-16 16:06
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  • C4 Vectors
    • Has both MAGNITUDE and DIRECTION
      • if equal have same magnitude and direction
      • Modulus = Magnitude
        • |a|
      • -a and a have same magnitude but opposite direction
        • Added using 'triangle law'
          • PQ + QP = 0
          • AB = a - bwhen a and b are position vectors of points A and B
    • Added using 'triangle law'
      • PQ + QP = 0
      • AB = a - bwhen a and b are position vectors of points A and B
    • Parallel
      • ta is parallel to a
      • t is a constant
      • ta + sb = qa + rb
        • a and b not parallel
        • t = q , s = r
      • t does not = 0
      • a.b=|a|*|b|
    • Position Vector
      • Of a point
      • From the origin
      • of point A - OA
      • often written simply as just a, b, c etc.
    • Cartesian Vectors
      • i
        • parallel to x axis
        • x increasing
      • j
        • parallel to y axis
        • y increasing
      • k
        • parallel to z axis
        • z increasing
    • Column Martix
      • ( x )( y )( z )
    • Angle Between two Vectors
      • cos? = |(a.b)/(|a|*|b|)|
        • acute
        • a and b are direction vectors of the lines
      • Perpendicular if a.b=0
    • a.b
      • a = a1i + a2j + a3k
      • b = b1i + b2j + b3k
      • = a1b1 + a2b2 + a3b3
    • Vector Equations
      • r = a + tb
        • passes through point A
        • parallel to vector b
      • r = c + t(d-c)
        • passes through points D and C
    • Distance / Modulus / Magnitude
      • Distance from origin to point (x,y,z)=sqrt(x^2+y^2+z^2)
      • of xi + yj is sqrt(x2 + y2)
    • Where Vectors Intersect
      • set equal to each other
      • solve first 2 to find t and s
      • sub t and s into 3 - if equal they intersect
  • Distance / Modulus / Magnitude
    • Distance from origin to point (x,y,z)=sqrt(x^2+y^2+z^2)
    • of xi + yj is sqrt(x2 + y2)

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