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Lesson: Parallel and Perpendicular Lines in Space

Worksheet • 9 Questions

Q1:

Which of the following vectors is not perpendicular to the line whose direction vector ⃑ π‘Ÿ is ( 6 , βˆ’ 5 ) ?

  • A ⃑ π‘Ÿ = ( 1 2 , βˆ’ 1 0 )
  • B ⃑ π‘Ÿ = ( 5 , 6 )
  • C ⃑ π‘Ÿ = ( 1 0 , 1 2 )
  • D ⃑ π‘Ÿ = ( βˆ’ 5 , βˆ’ 6 )

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

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.

  • Atrue
  • Bfalse

Q4:

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

  • A
  • B
  • C
  • D

Q5:

Given that οƒŸ 𝑀 = βˆ’ ⃑ 𝑖 βˆ’ 2 ⃑ 𝑗 , ⃑ 𝐿 = π‘Ž ⃑ 𝑖 βˆ’ 8 ⃑ 𝑗 , and οƒŸ 𝑀 β«½ ⃑ 𝐿 , where ⃑ 𝑖 and ⃑ 𝑗 are two perpendicular unit vectors, find the value of π‘Ž .

Q6:

Suppose A = ⟨ 1 , 3 , 2 ⟩ , B = ⟨ π‘˜ , 9 , π‘š ⟩ , C = ⟨ π‘˜ , π‘š , π‘˜ + π‘š ⟩ , and A B βˆ₯ , find | | C .

  • A 3 √ 1 4
  • B 3 √ 2
  • C √ 2
  • D √ 1 4

Q7:

Given the two vectors ⃑ 𝐴 = ο€» 8 ⃑ 𝑖 βˆ’ 7 ⃑ 𝑗 + ⃑ π‘˜  and ⃑ 𝐡 = ο€» 6 4 ⃑ 𝑖 βˆ’ 5 6 ⃑ 𝑗 + 8 ⃑ π‘˜  , determine whether these two vectors are parallel, perpendicular, or otherwise.

  • Aperpendicular
  • Bparallel
  • Cotherwise

Q8:

Find the values of π‘š and 𝑛 so that vector 2 ⃑ 𝑖 + 7 ⃑ 𝑗 + π‘š ⃑ π‘˜ is parallel to vector 6 ⃑ 𝑖 + 𝑛 ⃑ 𝑗 βˆ’ 2 1 ⃑ π‘˜ .

  • A π‘š = βˆ’ 7 , 𝑛 = 2 1
  • B π‘š = 1 . 7 , 𝑛 = βˆ’ 0 . 6
  • C π‘š = 2 . 3 , 𝑛 = βˆ’ 6 3
  • D π‘š = 2 1 , 𝑛 = βˆ’ 7

Q9:

Find the values of π‘š and 𝑛 so that vector 5 ⃑ 𝑖 + 4 ⃑ 𝑗 + π‘š ⃑ π‘˜ is parallel to vector 1 5 ⃑ 𝑖 + 𝑛 ⃑ 𝑗 βˆ’ 3 ⃑ π‘˜ .

  • A π‘š = βˆ’ 1 , 𝑛 = 1 2
  • B π‘š = 1 8 . 8 , 𝑛 = βˆ’ 2 5
  • C π‘š = 1 . 3 , 𝑛 = βˆ’ 9
  • D π‘š = 1 2 , 𝑛 = βˆ’ 1
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