10.2.1 Magnitude and direction of a vector Quiz: Pearson Edexcel Maths, Unit 10

The 20 questions

1. What is the notation for the magnitude of a vector a?

   • |a|
   • a^2
   • (a)
   • [a]

2. Which theorem is used to find the magnitude of a 2D vector?

   • Sine rule
   • Binomial theorem
   • Cosine rule
   • Pythagoras theorem

3. What trigonometric ratio typically finds the direction angle of a 2D vector?

   • arccos
   • arctan
   • arcsin
   • cosine

4. What is the magnitude of the unit vector in any direction?

   • -1
   • 0
   • 2
   • 1

5. How do you find a unit vector in the direction of vector a?

   • a plus |a|
   • |a| divided by a
   • a divided by |a|
   • a multiplied by |a|

6. What is the exact magnitude of the vector 5i - 12j?

   • 119
   • 17
   • 13
   • 7

7. If a vector is multiplied by a scalar of minus two, what happens to its magnitude?

   • Divided by 2
   • Squared
   • Multiplied by 2
   • Multiplied by -2

8. What is the magnitude of the zero vector?

   • 1
   • Undefined
   • 0
   • Infinity

9. What is the direction angle from the positive x-axis of the vector i + j?

   • 60 degrees
   • 30 degrees
   • 45 degrees
   • 90 degrees

10. What is the magnitude of the 3D vector 2i + 3j + 6k?

    • 11
    • 12
    • 49
    • 7

11. Which term describes a vector with a magnitude of one?

    • Position vector
    • Column vector
    • Zero vector
    • Unit vector

12. What is the horizontal component of a vector with magnitude 10 and angle 30 degrees to the x-axis?

    • 10 root 3
    • 5
    • 5 root 3
    • 5 root 2

13. What is the vertical component of a vector with magnitude 8 and angle 30 degrees to the x-axis?

    • 4 root 3
    • 2
    • 8 root 3
    • 4

14. If vector a has magnitude 4, what is the magnitude of vector minus 3a?

    • -12
    • 7
    • 1
    • 12

15. What is the magnitude of the column vector [ -6, 8 ]?

    • 14
    • 2
    • 100
    • 10

16. If |a| = 5, what is the magnitude of the vector 4a?

    • 5
    • 20
    • 80
    • 9

17. What is the exact magnitude of the 3D vector i - 2j + 2k?

    • 9
    • 3
    • 1
    • 5

18. What must be true for two vectors to have equal magnitudes and directions?

    • Vectors are equal
    • Vectors are negative
    • Vectors are unit
    • Vectors are parallel

19. What is the direction angle of the vector -i from the positive x-axis?

    • 0 degrees
    • 90 degrees
    • 270 degrees
    • 180 degrees

20. What is the direction angle from the positive x-axis of the vector -j?

    • 90 degrees
    • 270 degrees
    • 180 degrees
    • 360 degrees

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