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, 35).
120 · 35 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (60, 63).
60 · 63 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (80, 18).
80 · 18 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (45, 200).
45 · 200 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (12, 16).
12 · 16 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (30, 16).
30 · 16 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (36, 15).
36 · 15 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (120, 27).
120 · 27 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (32, 60).
32 · 60 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (10, 24).
10 · 24 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (48, 20).
48 · 20 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (14, 48).
14 · 48 · 2D vector magnitude

12 questions · Seed 46 · 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, 35).
125
|v| = √(120² + 35²) = √(14400 + 1225) = √15625 = 125.
2. Find the magnitude |v| of the vector v = (60, 63).
87
|v| = √(60² + 63²) = √(3600 + 3969) = √7569 = 87.
3. Find the magnitude |v| of the vector v = (80, 18).
82
|v| = √(80² + 18²) = √(6400 + 324) = √6724 = 82.
4. Find the magnitude |v| of the vector v = (45, 200).
205
|v| = √(45² + 200²) = √(2025 + 40000) = √42025 = 205.
5. Find the magnitude |v| of the vector v = (12, 16).
20
|v| = √(12² + 16²) = √(144 + 256) = √400 = 20.
6. Find the magnitude |v| of the vector v = (30, 16).
34
|v| = √(30² + 16²) = √(900 + 256) = √1156 = 34.
7. Find the magnitude |v| of the vector v = (36, 15).
39
|v| = √(36² + 15²) = √(1296 + 225) = √1521 = 39.
8. Find the magnitude |v| of the vector v = (120, 27).
123
|v| = √(120² + 27²) = √(14400 + 729) = √15129 = 123.
9. Find the magnitude |v| of the vector v = (32, 60).
68
|v| = √(32² + 60²) = √(1024 + 3600) = √4624 = 68.
10. Find the magnitude |v| of the vector v = (10, 24).
26
|v| = √(10² + 24²) = √(100 + 576) = √676 = 26.
11. Find the magnitude |v| of the vector v = (48, 20).
52
|v| = √(48² + 20²) = √(2304 + 400) = √2704 = 52.
12. Find the magnitude |v| of the vector v = (14, 48).
50
|v| = √(14² + 48²) = √(196 + 2304) = √2500 = 50.

12 questions · Seed 46 · 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, 35).
120 · 35 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (60, 63).
60 · 63 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (80, 18).
80 · 18 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (45, 200).
45 · 200 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (12, 16).
12 · 16 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (30, 16).
30 · 16 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (36, 15).
36 · 15 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (120, 27).
120 · 27 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (32, 60).
32 · 60 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (10, 24).
10 · 24 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (48, 20).
48 · 20 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (14, 48).
14 · 48 · 2D vector magnitude

12 questions · Seed 46 · 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, 35).
125
|v| = √(120² + 35²) = √(14400 + 1225) = √15625 = 125.
2. Find the magnitude |v| of the vector v = (60, 63).
87
|v| = √(60² + 63²) = √(3600 + 3969) = √7569 = 87.
3. Find the magnitude |v| of the vector v = (80, 18).
82
|v| = √(80² + 18²) = √(6400 + 324) = √6724 = 82.
4. Find the magnitude |v| of the vector v = (45, 200).
205
|v| = √(45² + 200²) = √(2025 + 40000) = √42025 = 205.
5. Find the magnitude |v| of the vector v = (12, 16).
20
|v| = √(12² + 16²) = √(144 + 256) = √400 = 20.
6. Find the magnitude |v| of the vector v = (30, 16).
34
|v| = √(30² + 16²) = √(900 + 256) = √1156 = 34.
7. Find the magnitude |v| of the vector v = (36, 15).
39
|v| = √(36² + 15²) = √(1296 + 225) = √1521 = 39.
8. Find the magnitude |v| of the vector v = (120, 27).
123
|v| = √(120² + 27²) = √(14400 + 729) = √15129 = 123.
9. Find the magnitude |v| of the vector v = (32, 60).
68
|v| = √(32² + 60²) = √(1024 + 3600) = √4624 = 68.
10. Find the magnitude |v| of the vector v = (10, 24).
26
|v| = √(10² + 24²) = √(100 + 576) = √676 = 26.
11. Find the magnitude |v| of the vector v = (48, 20).
52
|v| = √(48² + 20²) = √(2304 + 400) = √2704 = 52.
12. Find the magnitude |v| of the vector v = (14, 48).
50
|v| = √(14² + 48²) = √(196 + 2304) = √2500 = 50.

12 questions · Seed 46 · Age guidance, not curriculum certification