MathsAges 16-18

2D vector magnitude

Calculate the Euclidean magnitude |v| = √(x² + y²) of a 2D displacement vector. Review suitability for your learners before teaching.

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Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the magnitude |v| of the vector v = (120, 27).
120 · 27 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (8, 15).
8 · 15 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (3, 4).
3 · 4 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (12, 5).
12 · 5 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (84, 80).
84 · 80 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (7, 24).
7 · 24 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (15, 8).
15 · 8 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (21, 20).
21 · 20 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (16, 30).
16 · 30 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (80, 18).
80 · 18 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (63, 60).
63 · 60 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (96, 28).
96 · 28 · 2D vector magnitude

12 questions · Seed 42 · Age guidance, not curriculum certification

View the answer key

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. Find the magnitude |v| of the vector v = (120, 27).
123
|v| = √(120² + 27²) = √(14400 + 729) = √15129 = 123.
2. Find the magnitude |v| of the vector v = (8, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
3. Find the magnitude |v| of the vector v = (3, 4).
5
|v| = √(3² + 4²) = √(9 + 16) = √25 = 5.
4. Find the magnitude |v| of the vector v = (12, 5).
13
|v| = √(12² + 5²) = √(144 + 25) = √169 = 13.
5. Find the magnitude |v| of the vector v = (84, 80).
116
|v| = √(84² + 80²) = √(7056 + 6400) = √13456 = 116.
6. Find the magnitude |v| of the vector v = (7, 24).
25
|v| = √(7² + 24²) = √(49 + 576) = √625 = 25.
7. Find the magnitude |v| of the vector v = (15, 8).
17
|v| = √(15² + 8²) = √(225 + 64) = √289 = 17.
8. Find the magnitude |v| of the vector v = (21, 20).
29
|v| = √(21² + 20²) = √(441 + 400) = √841 = 29.
9. Find the magnitude |v| of the vector v = (16, 30).
34
|v| = √(16² + 30²) = √(256 + 900) = √1156 = 34.
10. Find the magnitude |v| of the vector v = (80, 18).
82
|v| = √(80² + 18²) = √(6400 + 324) = √6724 = 82.
11. Find the magnitude |v| of the vector v = (63, 60).
87
|v| = √(63² + 60²) = √(3969 + 3600) = √7569 = 87.
12. Find the magnitude |v| of the vector v = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the magnitude |v| of the vector v = (120, 27).
120 · 27 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (8, 15).
8 · 15 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (3, 4).
3 · 4 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (12, 5).
12 · 5 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (84, 80).
84 · 80 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (7, 24).
7 · 24 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (15, 8).
15 · 8 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (21, 20).
21 · 20 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (16, 30).
16 · 30 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (80, 18).
80 · 18 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (63, 60).
63 · 60 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (96, 28).
96 · 28 · 2D vector magnitude

12 questions · Seed 42 · Age guidance, not curriculum certification

Worksheet StudioAnswer key · Ages 16-18

Answers and reasoning. Review before teaching.

1. Find the magnitude |v| of the vector v = (120, 27).
123
|v| = √(120² + 27²) = √(14400 + 729) = √15129 = 123.
2. Find the magnitude |v| of the vector v = (8, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
3. Find the magnitude |v| of the vector v = (3, 4).
5
|v| = √(3² + 4²) = √(9 + 16) = √25 = 5.
4. Find the magnitude |v| of the vector v = (12, 5).
13
|v| = √(12² + 5²) = √(144 + 25) = √169 = 13.
5. Find the magnitude |v| of the vector v = (84, 80).
116
|v| = √(84² + 80²) = √(7056 + 6400) = √13456 = 116.
6. Find the magnitude |v| of the vector v = (7, 24).
25
|v| = √(7² + 24²) = √(49 + 576) = √625 = 25.
7. Find the magnitude |v| of the vector v = (15, 8).
17
|v| = √(15² + 8²) = √(225 + 64) = √289 = 17.
8. Find the magnitude |v| of the vector v = (21, 20).
29
|v| = √(21² + 20²) = √(441 + 400) = √841 = 29.
9. Find the magnitude |v| of the vector v = (16, 30).
34
|v| = √(16² + 30²) = √(256 + 900) = √1156 = 34.
10. Find the magnitude |v| of the vector v = (80, 18).
82
|v| = √(80² + 18²) = √(6400 + 324) = √6724 = 82.
11. Find the magnitude |v| of the vector v = (63, 60).
87
|v| = √(63² + 60²) = √(3969 + 3600) = √7569 = 87.
12. Find the magnitude |v| of the vector v = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.

12 questions · Seed 42 · Age guidance, not curriculum certification