Lesson Worksheet: 𝘯-Dimensional Vectors Mathematics

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In this worksheet, we will practice generalizing the concept of vectors to 𝑅ⁿ and applying the operations of vectors in 𝑅ⁿ.

Q1:

Find the unit vector of 𝐴, where 𝐴=⎡⎢⎢⎣−547−6⎤⎥⎥⎦.

  • A1442⎡⎢⎢⎣−547−6⎤⎥⎥⎦
  • B1442⎡⎢⎢⎣5476⎤⎥⎥⎦
  • C√1442⎡⎢⎢⎣−547−6⎤⎥⎥⎦
  • D√1414⎡⎢⎢⎣−547−6⎤⎥⎥⎦
  • E√1414⎡⎢⎢⎣5476⎤⎥⎥⎦

Q2:

If 𝐴=⎡⎢⎢⎢⎢⎣243−2−4⎤⎥⎥⎥⎥⎦, find |𝐴|.

  • A√7
  • B√15
  • C3
  • D49
  • E7

Q3:

If 𝐴=⎡⎢⎢⎢⎢⎣−51328⎤⎥⎥⎥⎥⎦ and 𝐵=⎡⎢⎢⎢⎢⎣12−124⎤⎥⎥⎥⎥⎦, find 𝐴−2𝐵.

  • A⎡⎢⎢⎢⎢⎣−6−1404⎤⎥⎥⎥⎥⎦
  • B⎡⎢⎢⎢⎢⎣−7−1420⎤⎥⎥⎥⎥⎦
  • C⎡⎢⎢⎢⎢⎣−3−35−20⎤⎥⎥⎥⎥⎦
  • D⎡⎢⎢⎢⎢⎣−7−35−20⎤⎥⎥⎥⎥⎦
  • E⎡⎢⎢⎢⎢⎣73−520⎤⎥⎥⎥⎥⎦

Q4:

If 𝐴=⎡⎢⎢⎢⎢⎣23−1−54⎤⎥⎥⎥⎥⎦, 𝐵=⎡⎢⎢⎢⎢⎣47475⎤⎥⎥⎥⎥⎦, and 𝐶=⎡⎢⎢⎢⎢⎣−1−38−2−7⎤⎥⎥⎥⎥⎦, find the value of |𝐴+𝐵−𝐶|.

  • A√103
  • B√199
  • C515
  • D√515
  • E103

Q5:

If 𝐴=⎡⎢⎢⎣6251⎤⎥⎥⎦, 𝐵=⎡⎢⎢⎣2−132⎤⎥⎥⎦, and 𝐶=⎡⎢⎢⎣3145⎤⎥⎥⎦, find 𝐴+2𝐵−2𝐶.

  • A⎡⎢⎢⎣7−270⎤⎥⎥⎦
  • B⎡⎢⎢⎣524−2⎤⎥⎥⎦
  • C⎡⎢⎢⎣4−23−5⎤⎥⎥⎦
  • D⎡⎢⎢⎣7270⎤⎥⎥⎦
  • E⎡⎢⎢⎣4235⎤⎥⎥⎦

Q6:

If 𝐴=⎡⎢⎢⎣5−364⎤⎥⎥⎦, find 2𝐴.

  • A⎡⎢⎢⎣106128⎤⎥⎥⎦
  • B⎡⎢⎢⎣106−128⎤⎥⎥⎦
  • C⎡⎢⎢⎣7−586⎤⎥⎥⎦
  • D⎡⎢⎢⎣10−6128⎤⎥⎥⎦
  • E⎡⎢⎢⎣7−186⎤⎥⎥⎦

Q7:

If 𝐴=⎡⎢⎢⎣−9−182⎤⎥⎥⎦ and 𝐵=⎡⎢⎢⎣2−383⎤⎥⎥⎦, find 𝐵−𝐴.

  • A⎡⎢⎢⎣−11201⎤⎥⎥⎦
  • B⎡⎢⎢⎣11−201⎤⎥⎥⎦
  • C⎡⎢⎢⎣720−1⎤⎥⎥⎦
  • D⎡⎢⎢⎣1120−1⎤⎥⎥⎦
  • E⎡⎢⎢⎣7−201⎤⎥⎥⎦

Q8:

If 𝐴=⎡⎢⎢⎢⎢⎣1−8745⎤⎥⎥⎥⎥⎦ and 𝐵=⎡⎢⎢⎢⎢⎣1−153−2⎤⎥⎥⎥⎥⎦, find 𝐴+𝐵.

  • A⎡⎢⎢⎢⎢⎣271277⎤⎥⎥⎥⎥⎦
  • B⎡⎢⎢⎢⎢⎣2−71273⎤⎥⎥⎥⎥⎦
  • C⎡⎢⎢⎢⎢⎣2−71277⎤⎥⎥⎥⎥⎦
  • D⎡⎢⎢⎢⎢⎣2−91277⎤⎥⎥⎥⎥⎦
  • E⎡⎢⎢⎢⎢⎣2−91273⎤⎥⎥⎥⎥⎦

Q9:

Find the unit vector in the same direction as the vector 26.

  • A⎡⎢⎢⎣√10√103⎤⎥⎥⎦
  • B⎡⎢⎢⎣120320⎤⎥⎥⎦
  • C⎡⎢⎢⎢⎣√10103√1010⎤⎥⎥⎥⎦
  • D11
  • E⎡⎢⎢⎢⎢⎣2√86√8⎤⎥⎥⎥⎥⎦

Q10:

Compute 5⟨1,2+3𝑖,3,−2⟩+6⟨2−𝑖,1,−2,7⟩.

  • A⟨33−11𝑖,33+33𝑖,11,55⟩
  • B⟨13−6𝑖,8+3𝑖,−9,40⟩
  • C⟨17−6𝑖,16+15𝑖,3,32⟩
  • D⟨7−𝑖,11+15𝑖,13,−3⟩
  • E⟨3−𝑖,3+3𝑖,1,5⟩

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