# C4 Vectors Summery

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• Created by: Tassillow
• Created on: 28-05-16 16:06
• 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
• PQ + QP = 0
• AB = a - bwhen a and b are position vectors of points A and B
• 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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