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.

  • A957ijk
  • B11420ijk
  • C11+19ijk
  • D91120ijk

Q2:

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

  • A8,25,185
  • B8,25,185
  • C85,25,185

Q3:

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

  • A0,5,52
  • B3,2,112
  • C10,0,15
  • D5,0,152

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||||VW
  • C||VW

Q5:

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

  • A73+133ij
  • B73133ij
  • C253133+163ijk
  • D7313ij

Q6:

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

  • A3+3ik
  • Bijk2+3
  • Cij2
  • Dijk2+5
  • E3+3ij

Q7:

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

  • A1
  • B2
  • C23
  • D32
  • E22

Q8:

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

  • Ai
  • B89jk
  • Cijk8+9
  • D28+9ijk

Q9:

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

  • A35,35
  • B155,155
  • C15,15
  • D15,15

Q10:

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

  • A116,116
  • B116121,116121
  • C22911,22911
  • D229,229

Q11:

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

  • A4141(2+6)ijk
  • B8585(2+9)ik
  • C721(2+6)ijk
  • D4141(26+)ijk

Q12:

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

  • A5,7,1
  • B1,1,1
  • C13,753,153
  • D13,753,153

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