Lesson Worksheet: Magnitude of a Vector in 3D Mathematics

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

Q1:

True or False: The magnitude of a 3D vector represents the length of the vector.

  • ATrue
  • BFalse

Q2:

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

  • A1
  • B33
  • C33
  • D1

Q3:

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

  • A2
  • B4
  • C6
  • D14
  • E23

Q4:

Which of these vectors has the greatest magnitude?

  • A3ik
  • Bijk+
  • Cij+
  • D2+3ijk
  • E32ik

Q5:

Which of these vectors has the least magnitude?

  • A2,4,5
  • B1,7,2
  • C3,5,6
  • D3,1,7
  • E4,6,7

Q6:

If A=5,7,2 and B=6,2,1, determine |+|AB rounded to one decimal place.

Q7:

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

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

Q8:

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

  • A118
  • B26
  • C26
  • D118

Q9:

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

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

Q10:

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

  • A4,4
  • B817
  • C10
  • D817

This lesson includes 24 additional questions and 203 additional question variations for subscribers.

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