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Worksheet: Intersections of Lines and Planes

Q1:

Which of the following statements is true about the two planes?

  • A The two planes are parallel.
  • B The two planes are coincident.
  • C The two planes are intersected.

Q2:

Which of the following is a plane that is parallel to 𝐴 𝐡 𝐢 𝐷 ?

  • A plane 𝐴 𝐡 𝐡 β€² 𝐴 β€²
  • B plane 𝐢 𝐷 𝐷 β€² 𝐢 β€²
  • C plane 𝐡 𝐢 𝐢 β€² 𝐡 β€²
  • D plane 𝐴 β€² 𝐡 β€² 𝐢 β€² 𝐷 β€²
  • E plane 𝐴 𝐷 𝐷 β€² 𝐴 β€²

Q3:

Using the cube below, decide which of the following describe the relative position of the planes 𝐴 β€² 𝐡 β€² 𝐡 𝐴 and 𝐴 β€² 𝐡 β€² 𝐢 𝐷 .

  • A perpendicular
  • B parallel
  • C skew
  • D intersecting

Q4:

Using the cube below, decide which of the following describe the relative position of the planes 𝐴 𝐡 𝐡 β€² 𝐴 β€² and 𝐷 𝐢 𝐢 β€² 𝐷 β€² .

  • A perpendicular
  • B intersecting
  • C skew
  • D parallel

Q5:

Find three planes that pass through both of the points 𝐡 and 𝐢 .

  • A 𝐡 𝐢 𝐢 β€² , 𝐡 𝐢 𝐷 , 𝐴 𝐡 𝐡 β€²
  • B 𝐡 𝐢 𝐷 , 𝐴 𝐷 𝐷 β€² , 𝐴 β€² 𝐷 β€² 𝐢 β€²
  • C 𝐡 𝐢 𝐢 β€² , 𝐡 𝐢 𝐷 , 𝐢 𝐷 𝐢 β€²
  • D 𝐡 𝐢 𝐷 , 𝐡 𝐢 𝐢 β€² , 𝐡 𝐢 𝐷 β€²

Q6:

Using the cube below, decide which of the following describe the relative position of the planes 𝐴 𝐡 𝐢 and 𝐴 β€² 𝐡 β€² 𝐷 .

  • A perpendicular
  • B parallel
  • C skew
  • D intersecting

Q7:

In the following figure, determine the intersection of plane 𝐴 𝐷 𝐡 and plane 𝐡 𝐢 𝐢 β€² 𝐡 β€² .

  • A βƒ–     βƒ— 𝐷 𝐢
  • B βƒ–     βƒ— 𝐡 𝐢
  • C βƒ–     βƒ— 𝐴 𝐡
  • D βƒ–     βƒ— 𝐡 𝐷

Q8:

In the following figure, determine the intersection of plane 𝐴 𝐷 𝐴 β€² and plane 𝐡 𝐷 𝐡 β€² .

  • A βƒ–        βƒ— 𝐴 β€² 𝐡 β€²
  • B { 𝐷 }
  • C βƒ–     βƒ— 𝐴 𝐡
  • D βƒ–       βƒ— 𝐢 𝐢 β€²

Q9:

Determine the intersection of plane X with plane ABC.

  • A βƒ–     βƒ— 𝐴 𝐢
  • B βƒ– βƒ— 𝐿
  • C { 𝐴 }
  • D βƒ–     βƒ— 𝐴 𝐡

Q10:

In the following figure, determine the intersection of plane 𝐴 𝐷 𝐡 and plane 𝐴 𝐡 𝐢 .

  • A βƒ–     βƒ— 𝐴 𝐢
  • B βƒ–     βƒ— 𝐷 𝐢
  • C βƒ–     βƒ— 𝐷 𝐡
  • D βƒ–     βƒ— 𝐴 𝐡