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Worksheet: Parallel and Perpendicular Lines in Space

Q1:

Which of the following vectors is not perpendicular to the line whose direction vector is ?

  • A
  • B
  • C
  • D

Q2:

In the figure, 𝐴 𝐻 is perpendicular to the plane π‘Œ , which contains the points 𝐻 , 𝐡 , 𝐢 , 𝐷 a n d . If 𝐡 𝐷 = 3 6 and 𝐴 𝐷 = 8 5 , find the area of β–³ 𝐴 𝐡 𝐷 .

  • A 3 272.5
  • B 1 530
  • C 3 060
  • D 1 386

Q3:

Determine whether the following is true or false: If the component of a vector in the direction of another vector is zero, then the two are parallel.

  • Afalse
  • Btrue

Q4:

Given that , , and , find the relation between and .

  • A
  • B
  • C
  • D

Q5:

Given that M i j = βˆ’ βˆ’ 2 , L i j = π‘Ž βˆ’ 8 , and M L βˆ₯ , where i and j are two perpendicular unit vectors, find the value of π‘Ž .

Q6:

Suppose , , , and , find .

  • A
  • B
  • C
  • D

Q7:

Given the two vectors and , determine whether these two vectors are parallel, perpendicular, or otherwise.

  • Aotherwise
  • Bperpendicular
  • Cparallel

Q8:

Find the values of and so that vector is parallel to vector .

  • A ,
  • B ,
  • C ,
  • D ,

Q9:

Find the values of and so that vector is parallel to vector .

  • A ,
  • B ,
  • C ,
  • D ,