vectors

• define vector

  a quantity with both magnitude and direction written as: where A & B are points on the line and x and y are co-ordinates

  
• Define magnitude


  the size of a vector written as : where A and B are points on the line

  
• State how to find the magnitude

  
• Define zero vector


  vector with a magnitude equal to 0 meaning v=0 and x,y,z = 0
• Define unit vector

  A vector with a magnitude of 1, meaning it is equal to 1
• Describe what happens when a vector is multiplied by a scalar

  the resultant vector is equal to kv. where v is the vector and k is the scalar. This means the vector will have the same direction but the magnitude will be k times longer.
• State the magnitude of a vector multiplied by a scalar

  k|v|. found with the normal magnitude process, then multiplying magnitude by the scalar.
• Define position vector


  vector which describes how to get from the origin (O) to the point or from one point to another

  
• State how to use the position vector to find another point


  Find the equations for the vectors and rearrange
• State the process for collinearity

  1. find the values of all the possible vectors (chimney co-ordinates)

  2. divide all the xs and all the ys by each other

  3. if the value obtained is the same, they are collinear

  4. if they are collinear write, kv = a therefore are parallel. since ... is a common point, the points are collinear
• State the process to use the section formula to find the co-ordinates of a point on a line

  1. find the ratio at which the line is split by the point (P divides AB in 1:3)

  2. state the distance between end point of the line and the point in the line (1/4 AB = AP)

  3. rearrange (1/4(b-a)=p-a)

  4. rearrange again (1/4(b-a) + a = p)

  5. sub in values and find the point

  6. state the co-ordinates found (P(x,y))
• Describe basis vectors


  define the vector in terms of i,j and k/ vector = xi + yj + zk
• State the dot product formulae


  - vectors must travel AWAY from the angle

  - angle must be between 0 and 180

  - if two vectors are perpendicular, dot product is 0

  
• State the angle in the dot product formula

  
• State the properties of the dot product


  - a.b = b.a

  - a.(b+c) = a.b + a.c

  - if a.(b+c) = 0 then a is perpendicular to b and c
• State the process to calculate a.(b+c) when the magnitudes are known


  1. a.(b+c) = a.b + a.c

  2. a.b + a.c = |a||b|cosx + |a||c|cosx

  3. state the answer