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Worksheet: Equation of a Plane in Space in Vector Form

Q1:

Which of the following planes contains the straight line ?

  • A
  • B
  • C
  • D
  • E

Q2:

Write, in normal form, the equation of the plane ( 1 , 0 , 3 ) , ( 1 , 2 , βˆ’ 1 ) and ( 6 , 1 , 6 ) .

  • A π‘₯ βˆ’ 2 𝑦 βˆ’ 𝑧 βˆ’ 2 = 0
  • B π‘₯ + 3 𝑧 + 2 0 = 0
  • C π‘₯ + 3 𝑧 βˆ’ 2 0 = 0
  • D π‘₯ βˆ’ 2 𝑦 βˆ’ 𝑧 + 2 = 0
  • E π‘₯ βˆ’ 2 𝑦 βˆ’ 𝑧 βˆ’ 4 = 0

Q3:

Find the vector form of the equation of the straight line 4 π‘₯ βˆ’ 3 βˆ’ 9 = 7 𝑦 βˆ’ 8 βˆ’ 2 = 7 + 6 𝑧 4 .

  • A r =  4 3 , 7 8 , βˆ’ 6 7 ο‡· + 𝑑  βˆ’ 4 9 , βˆ’ 7 2 , 3 2 ο‡·
  • B r =  βˆ’ 9 4 , βˆ’ 2 7 , 2 3 ο‡· + 𝑑  3 4 , 8 7 , βˆ’ 7 6 ο‡·
  • C r =  βˆ’ 3 4 , βˆ’ 8 7 , 7 6 ο‡· + 𝑑  9 4 , 2 7 , βˆ’ 2 3 ο‡·
  • D r =  3 4 , 8 7 , βˆ’ 7 6 ο‡· + 𝑑  βˆ’ 9 4 , βˆ’ 2 7 , 2 3 ο‡·