Worksheet: Parallel and Perpendicular Vectors in Space

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

Q1:

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

Q2:

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

  • A 𝑥 = 𝑦
  • B 𝑥 𝑦 = 3 6 1
  • C 𝑥 = 𝑦
  • D 𝑥 𝑦 = 3 6 1

Q3:

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

Q4:

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

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

Q5:

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

  • Aparallel
  • Bperpendicular
  • Cotherwise

Q6:

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

  • A 𝑚 = 7 , 𝑛 = 2 1
  • B 𝑚 = 2 . 3 , 𝑛 = 6 3
  • C 𝑚 = 2 1 , 𝑛 = 7
  • D 𝑚 = 1 . 7 , 𝑛 = 0 . 6

Q7:

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

Q8:

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

  • A r = 1 2 , 1 0
  • B r = 5 , 6
  • C r = 5 , 6
  • D r = 1 0 , 1 2

Q9:

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

Q10:

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

Q11:

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

  • A 2 5 2 4
  • B 2 4 2 5
  • C 2 4 2 5
  • D 2 5 2 4

Q12:

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

  • Aperpendicular
  • Bparallel

Nagwa uses cookies to ensure you get the best experience on our website. Learn more about our Privacy Policy.