Worksheet: Vector Operations in 3D

In this worksheet, we will practice doing operations on vectors in 3D, such as addition, subtraction, and scalar multiplication.

Q1:

If Aijk=58+6 and Bijk=43+13, find AB.

  • A 9 5 7 i j k
  • B 1 1 4 2 0 i j k
  • C 1 1 + 1 9 i j k
  • D 9 1 1 2 0 i j k

Q2:

If A=8,9,9 and B=6,4,9, find 2545AB.

  • A 8 , 2 5 , 1 8 5
  • B 8 , 2 5 , 1 8 5
  • C 8 5 , 2 5 , 1 8 5

Q3:

If A=1,1,1, and B=1,1,2, determine the vector C for which 2+5=5CAB.

  • A 0 , 5 , 5 2
  • B 3 , 2 , 1 1 2
  • C 1 0 , 0 , 1 5
  • D 5 , 0 , 1 5 2

Q4:

V and W are two vectors, where V=1,5,2 and W=3,1,1. Comparing ||VW and ||||VW, which quantity is larger?

  • AThey are both the same.
  • B | | | | V W
  • C | | V W

Q5:

If Aijk=97+8 and Bijk=83+4, find AB23.

  • A 7 3 + 1 3 3 i j
  • B 7 3 1 3 3 i j
  • C 2 5 3 1 3 3 + 1 6 3 i j k
  • D 7 3 1 3 i j

Q6:

If Aijk=++, Bijk=2+3, and Cijk=+, find ABC+.

  • A 3 + 3 i k
  • B i j k 2 + 3
  • C i j 2
  • D i j k 2 + 5
  • E 3 + 3 i j

Q7:

If Aijk=+2, Bjk=+, and Cik=, find ||ABC.

  • A1
  • B2
  • C 2 3
  • D 3 2
  • E 2 2

Q8:

Suppose that A=4,7,7, B=5,1,2, and ABCi++=. What is C?

  • A i
  • B 8 9 j k
  • C i j k 8 + 9
  • D 2 8 + 9 i j k

Q9:

Given that Aijk=3++𝑚 and that B is a unit vector equal to 15A, determine the possible values of 𝑚.

  • A 3 5 , 3 5
  • B 1 5 5 , 1 5 5
  • C 1 5 , 1 5
  • D 1 5 , 1 5

Q10:

Suppose a unit vector A is such that 11=1,2,𝑘A. Determine the possible values of 𝑘.

  • A 1 1 6 , 1 1 6
  • B 1 1 6 1 2 1 , 1 1 6 1 2 1
  • C 2 2 9 1 1 , 2 2 9 1 1
  • D 2 2 9 , 2 2 9

Q11:

Given Ajk=3+5 and Bijk=2+3+4, determine the unit vector in the direction BA.

  • A 4 1 4 1 ( 2 + 6 ) i j k
  • B 8 5 8 5 ( 2 + 9 ) i k
  • C 7 2 1 ( 2 + 6 ) i j k
  • D 4 1 4 1 ( 2 6 + ) i j k

Q12:

Find the unit vector in the direction of 𝐴𝐵, where 𝐴4,5,2 and 𝐵9,2,3.

  • A 5 , 7 , 1
  • B 1 , 1 , 1
  • C 1 3 , 7 5 3 , 1 5 3
  • D 1 3 , 7 5 3 , 1 5 3

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