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.

  • A 1
  • B33
  • C 3 3
  • D1

Q2:

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

  • A 1 + 6
  • B 1 7
  • C5
  • D 3 5

Q3:

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

  • A 9
  • B53
  • C 5 3
  • D81

Q4:

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

  • A5
  • B27
  • C 3 3
  • D25

Q5:

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

  • A 1 + 5
  • B 2 6
  • C 3 2
  • D 5 + 1 3

Q6:

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

  • A 4 , 4
  • B 8 1 7
  • C 1 0
  • D 8 1 7

Q7:

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

  • A252
  • B 2 4 1
  • C 2 3
  • D23

Q8:

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

  • A 4 1
  • B7
  • C 1 8 5
  • D41

Q9:

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

  • A 4 9 , 4 9
  • B9
  • C 9 , 9
  • D4

Q10:

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

  • A118
  • B 2 6
  • C26
  • D 1 1 8

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
  • B 2
  • C 3
  • D 2 2
  • E1

Q13:

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

  • A2
  • B4
  • C 6
  • D 1 4
  • E 2 3

Q14:

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

  • A2
  • B 6 , 6
  • C6
  • D 6
  • E 2 , 2

Q15:

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

  • A6
  • B 3 6
  • C 2 6
  • D i k + 5
  • E i j k + + 5

Q16:

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

  • A 3 2
  • B3
  • C 3 3

Q17:

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

  • A | + | = 3 A B , | | + | | = 1 + 2 A B
  • B | + | = 3 2 A B , | | + | | = 2 + 2 A B
  • C | + | = 3 5 A B , | | + | | = 5 + 3 0 A B

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
  • B 4 6
  • C 5
  • D 8

Q20:

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

  • A v v
  • B v
  • C v v
  • D v

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