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OABC is a trapezium.

D is the point on OB such that OD : DB = 2:3

E is the point on BC such that BE : EC = 1:4

Work out the vector of DE in terms of a & b. Give your answer in its simplest form. ​

OABC is a trapezium D is the point on OB such that OD DB 23E is the point on BC such that BE EC 14Work out the vector of DE in terms of a amp b Give your answer class=

Respuesta :

mhanifa

Answer:

  • DE = 2/5a + b

Step-by-step explanation:

Find OB:

  • OB = a + b

Find BC:

  • OB + BC = OC
  • a + b + BC = 3b
  • BC = 2b - a

Find DB:

  • OD/DB = 2/3 ⇒ OD + DB = OB ⇒ 2x + 3x = OB ⇒ 5x = OB ⇒ x = OB/5
  • DB = 3x = 3/5 OB = 3/5(a + b)

Find BE:

  • BE/EC = 1/4 ⇒ BE + EC = BC ⇒ x + 4x = BC ⇒ 5x = BC ⇒ x = 1/5 BC
  • BE = x ⇒ BE = 1/5 BC ⇒ BE = 1/5(2b - a)

Find DE:

  • DE = DB + BE
  • DE = 3/5(a + b) +  1/5(2b - a)
  • DE = 1/5(3a + 3b + 2b - a)
  • DE = 1/5(2a + 5b)
  • DE = 2/5a + b

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