Worksheet: Equation of a Plane in Space in Vector Form

In this worksheet, we will practice finding the vector form of the equation of a plane in space.

Q1:

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

  • A 𝑥 2 𝑦 𝑧 2 = 0
  • B 𝑥 + 3 𝑧 + 2 0 = 0
  • C 𝑥 + 3 𝑧 2 0 = 0
  • D 𝑥 2 𝑦 𝑧 + 2 = 0
  • E 𝑥 2 𝑦 𝑧 4 = 0

Q2:

Find the vector form of the equation of the straight line 4 𝑥 3 9 = 7 𝑦 8 2 = 7 + 6 𝑧 4 .

  • A 𝑟 = 4 3 , 7 8 , 6 7 + 𝑡 4 9 , 7 2 , 3 2
  • B 𝑟 = 9 4 , 2 7 , 2 3 + 𝑡 3 4 , 8 7 , 7 6
  • C 𝑟 = 3 4 , 8 7 , 7 6 + 𝑡 9 4 , 2 7 , 2 3
  • D 𝑟 = 3 4 , 8 7 , 7 6 + 𝑡 9 4 , 2 7 , 2 3

Q3:

Which of the following planes contains the straight line ?

  • A
  • B
  • C
  • D
  • E

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