# 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'

- 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

- i
- 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

- cos? = |(a.b)/(|a|*|b|)|
- 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

- r = a + tb
- 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

- Has both MAGNITUDE and DIRECTION
- 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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