Worksheet: Parallel and Perpendicular Vectors in Space

In this worksheet, we will practice recognizing parallel and perpendicular vectors in space.


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


Given that A=𝑥,19, B=19,𝑦, and AB, find the relation between 𝑥 and 𝑦.

  • A𝑥=𝑦
  • B𝑥𝑦=361
  • C𝑥=𝑦
  • D𝑥𝑦=361


Given that Mij=2, Lij=𝑎8, and ML, where i and j are two perpendicular unit vectors, find the value of 𝑎.


Suppose A=1,3,2, B=𝑘,9,𝑚, C=𝑘,𝑚,𝑘+𝑚, and AB, find ||C.

  • A2
  • B314
  • C14
  • D32


Given the two vectors Aijk=(87+) and Bijk=(6456+8), determine whether these two vectors are parallel, perpendicular, or otherwise.

  • Aparallel
  • Bperpendicular
  • Cotherwise


Find the values of 𝑚 and 𝑛 so that vector 2+7+𝑚ijk is parallel to vector 6+𝑛21ijk.

  • A𝑚=7, 𝑛=21
  • B𝑚=2.3, 𝑛=63
  • C𝑚=21, 𝑛=7
  • D𝑚=1.7, 𝑛=0.6


In the figure, 𝐴𝐻 is perpendicular to the plane 𝑌, which contains the points 𝐻, 𝐵, 𝐶, and 𝐷. If 𝐵𝐷=36 and 𝐴𝐷=85, find the area of 𝐴𝐵𝐷.

  • A1,386
  • B3,272.5
  • C3,060
  • D1,530


Which of the following vectors is not perpendicular to the line whose direction vector r is 6,5?

  • Ar=12,10
  • Br=5,6
  • Cr=5,6
  • Dr=10,12


If the straight line 𝑥+810=𝑦+8𝑚=𝑧+108 is perpendicular to 𝑥+54=𝑦+810, and 𝑧=8, find 𝑚.


If the straight line 𝑥106=𝑦+68=𝑧+2𝑘 is parallel to 𝑥112=𝑦+3𝑚=𝑧+114, find 𝑘+𝑚.


If the two straight lines 𝑥+38=𝑦44𝑛=𝑧+110 and 𝑥+54𝑛=𝑦+104=𝑧35 are perpendicular, find 𝑛.

  • A2524
  • B2425
  • C2425
  • D2524


Given that A and B satisfy AB0×=, A0 and B0. How are the two vectors related?

  • Aperpendicular
  • Bparallel

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