Worksheet: Magnitude of a Vector in 3D

In this worksheet, we will practice finding the norm of a position vector in space.

Q1:

If A=2,5,2, find ||A.

  • A1
  • B33
  • C33
  • D1

Q2:

If A=2,1,0 and B=2,0,4, determine ||+||AB.

  • A1+6
  • B17
  • C5
  • D35

Q3:

If A=1,4,6, find ||A.

  • A9
  • B53
  • C53
  • D81

Q4:

If A=5,1,1, find ||A.

  • A5
  • B27
  • C33
  • D25

Q5:

If A=0,3,2 and B=1,0,2, determine ||+||AB.

  • A1+5
  • B26
  • C32
  • D5+13

Q6:

Given that A=6,4,𝑘 and ||=217A units, determine the possible values of 𝑘.

  • A4,4
  • B817
  • C10
  • D817

Q7:

Given that ||=6A, ||=3B, ||=14C, and all three vectors are mutually perpendicular, determine |++|ABC.

  • A252
  • B241
  • C23
  • D23

Q8:

Given that 𝐴𝐵=5+24ijk and 𝐵𝐶=4+4+6ijk, determine ||𝐴𝐶||.

  • A41
  • B7
  • C185
  • D41

Q9:

Given that |𝑥4,4,7|=4, find the value of 𝑥.

  • A9
  • B4
  • C9,9
  • D49,49

Q10:

Given that AB+=2,4,3 and A=3,5,3, determine ||B.

  • A118
  • B26
  • C26
  • D118

Q11:

Suppose A and B are two vectors in . Is |+|=||+||ABAB? If not, which is greater?

  • Ano, ||+||AB
  • Bno, |+|AB
  • Cyes

Q12:

If Aijk=+, find ||A.

  • A3
  • B2
  • C3
  • D22
  • E1

Q13:

If Aijk=2+3, find ||A.

  • A2
  • B4
  • C6
  • D14
  • E23

Q14:

If Aijk=𝑎+ and ||=6A, find all the possible values of 𝑎.

  • A2
  • B6,6
  • C6
  • D6
  • E2,2

Q15:

If Aijk=+2+ and Bijk=22+4, find ||+||AB.

  • A6
  • B36
  • C26
  • Dik+5
  • Eijk++5

Q16:

If Aijk=4+45 and Bik=3, determine ||AB.

  • A32
  • B3
  • C33

Q17:

If Aijk=52 and Bjk=+2, determine |+|AB and ||+||AB.

  • A|+|=3AB, ||+||=1+2AB
  • B|+|=32AB, ||+||=2+2AB
  • C|+|=35AB, ||+||=5+30AB

Q18:

Is A=23,23,14 a unit vector?

  • ANo
  • BYes

Q19:

Given that the coordinates of A and B are 1,2,2 and 1,2,3, respectively, determine |2+|AB.

  • A5
  • B46
  • C5
  • D8

Q20:

Which of the following computes the length of the vector v?

  • Avv
  • Bv
  • Cvv
  • Dv

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