Maths Vector Question

• symx

  27 Oct 08, 21:56

  

  Do kindly help me in this question, thank you.

• skythewood

  27 Oct 08, 23:13

  i)

  OC = OB + BC
        =  OB + 3OA       (BC = 3OA)

   

  AP = 1/4 AB               (given)
        = 1/4 (AO + OB)    
        = 1/4 (OB -OA)

   

  OP = OA + AP

  ii)

  O, P and C together forms a straight line

  iii)

  find |PA|, and |BA|.

  area of triangle is 1/2 x base x height.

  for OAP, 1/2 x |PA| x height

  for OBP, 1/2 x |BA| x height

  for both triangle, the height is the same

• XxHoWxX

  27 Oct 08, 23:15

  i)(a) OC= OB +BC

                 = b + 3 OA

                 = b + 3a

  i)(b) AP = 1/4 (OB - OA)

                  = 1/4 (b - a)

  i)(c) OP = OA + AP

                   = a + 1/4 (b - a)

                   = a + 1/4 b - 1/4 a

                   = 1/4 (3a + b)

  ii) OPC is a straight line as OP is 1/4 of OC.

  iii) I do not know how to do this.

• symx

  28 Oct 08, 00:52

  !)

  
  

  AP = 1/4 AB               (given)
        = 1/4 (AO + OB)    
        = 1/4 (OB -OA)

  Why AO must invert into OA? Is it because value have to be read off from the origin which is O.

• skythewood

  28 Oct 08, 00:58

  directions is important for vectors. AO = -OA.

  note the negative sign...

  OA = a

  AO = -a

• symx

  28 Oct 08, 01:03

  Oh I c, if values must read off from origin and by doing so for AO. AO will need to be inverted and thus the value become negative. Am I right?

• skythewood

  28 Oct 08, 01:08

  no.

  the arrow thingie on the diagram says OA is vector a.

  OA means go from O to A.

  if you go from A to O, the vector is -a

  not because of origins.

• symx

  28 Oct 08, 01:11

  Ok, I understand some parts but I still have quesiton on this segments.

• symx

  28 Oct 08, 19:58

   

  1)

  C)

  OP = OA + AP

  I don't get the answer which is 1/4(b+3a) and also for part 3 the answer is 1/3. What value should I sub into |PA| and |BA|?

   

• skythewood

  28 Oct 08, 20:03

  AP = 1/4 (OB -OA), from 1B)

  OP = OA + AP
         = OA + 1/4(OB - OA)
         =  OA + 1/4OB - 1/4OA
         = 3/4OA + 1/4OB
         = 1/4( 3OA + OB)
         = 1/4 (3a + b)                  (from diagram, OA = a, OB = b)

   

• skythewood

  28 Oct 08, 20:16

  |PA| means modulus of the vector PA. this mean find it's length.of vector PA. direction is no longer important as either direction will have the same length.

  length of AP, |AP| = |1/4(b-a)|
                                 =  1/4   |b-a|

  BP = BO + OP
        = -OB + OP
       = -b   +   1/4(3a + b)
       = -b   +3/4a +1/4b
       = 3/4a - 3/4b

  |BP| = |3/4a - 3/4b|
          =3/4  |a-b|
          = 3/4  |b-a|                                   |b-a| = |a-b|, since direction don't matters

  hence |BP| is 3 times bigger than |AP|

   

• symx

  28 Oct 08, 22:39

  Thank you very much for your help.