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.

Choose “Save as PDF” to keep a copy. Use your browser’s paper setting for A4 or Letter.

Worksheet StudioPractice pack · Ages 16-18

Take your time. Show your thinking.

1. Find the magnitude |v| of the vector v = (48, 14).
48 · 14 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (42, 40).
42 · 40 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (100, 105).
100 · 105 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (96, 28).
96 · 28 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (15, 8).
15 · 8 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (36, 15).
36 · 15 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (200, 45).
200 · 45 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (24, 45).
24 · 45 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (5, 12).
5 · 12 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (8, 15).
8 · 15 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (7, 24).
7 · 24 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (18, 80).
18 · 80 · 2D vector magnitude

12 questions · Seed 45 · 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 = (48, 14).
50
|v| = √(48² + 14²) = √(2304 + 196) = √2500 = 50.
2. Find the magnitude |v| of the vector v = (42, 40).
58
|v| = √(42² + 40²) = √(1764 + 1600) = √3364 = 58.
3. Find the magnitude |v| of the vector v = (100, 105).
145
|v| = √(100² + 105²) = √(10000 + 11025) = √21025 = 145.
4. Find the magnitude |v| of the vector v = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.
5. Find the magnitude |v| of the vector v = (15, 8).
17
|v| = √(15² + 8²) = √(225 + 64) = √289 = 17.
6. Find the magnitude |v| of the vector v = (36, 15).
39
|v| = √(36² + 15²) = √(1296 + 225) = √1521 = 39.
7. Find the magnitude |v| of the vector v = (200, 45).
205
|v| = √(200² + 45²) = √(40000 + 2025) = √42025 = 205.
8. Find the magnitude |v| of the vector v = (24, 45).
51
|v| = √(24² + 45²) = √(576 + 2025) = √2601 = 51.
9. Find the magnitude |v| of the vector v = (5, 12).
13
|v| = √(5² + 12²) = √(25 + 144) = √169 = 13.
10. Find the magnitude |v| of the vector v = (8, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
11. Find the magnitude |v| of the vector v = (7, 24).
25
|v| = √(7² + 24²) = √(49 + 576) = √625 = 25.
12. Find the magnitude |v| of the vector v = (18, 80).
82
|v| = √(18² + 80²) = √(324 + 6400) = √6724 = 82.

12 questions · Seed 45 · 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 = (48, 14).
48 · 14 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (42, 40).
42 · 40 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (100, 105).
100 · 105 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (96, 28).
96 · 28 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (15, 8).
15 · 8 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (36, 15).
36 · 15 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (200, 45).
200 · 45 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (24, 45).
24 · 45 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (5, 12).
5 · 12 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (8, 15).
8 · 15 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (7, 24).
7 · 24 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (18, 80).
18 · 80 · 2D vector magnitude

12 questions · Seed 45 · 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 = (48, 14).
50
|v| = √(48² + 14²) = √(2304 + 196) = √2500 = 50.
2. Find the magnitude |v| of the vector v = (42, 40).
58
|v| = √(42² + 40²) = √(1764 + 1600) = √3364 = 58.
3. Find the magnitude |v| of the vector v = (100, 105).
145
|v| = √(100² + 105²) = √(10000 + 11025) = √21025 = 145.
4. Find the magnitude |v| of the vector v = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.
5. Find the magnitude |v| of the vector v = (15, 8).
17
|v| = √(15² + 8²) = √(225 + 64) = √289 = 17.
6. Find the magnitude |v| of the vector v = (36, 15).
39
|v| = √(36² + 15²) = √(1296 + 225) = √1521 = 39.
7. Find the magnitude |v| of the vector v = (200, 45).
205
|v| = √(200² + 45²) = √(40000 + 2025) = √42025 = 205.
8. Find the magnitude |v| of the vector v = (24, 45).
51
|v| = √(24² + 45²) = √(576 + 2025) = √2601 = 51.
9. Find the magnitude |v| of the vector v = (5, 12).
13
|v| = √(5² + 12²) = √(25 + 144) = √169 = 13.
10. Find the magnitude |v| of the vector v = (8, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
11. Find the magnitude |v| of the vector v = (7, 24).
25
|v| = √(7² + 24²) = √(49 + 576) = √625 = 25.
12. Find the magnitude |v| of the vector v = (18, 80).
82
|v| = √(18² + 80²) = √(324 + 6400) = √6724 = 82.

12 questions · Seed 45 · Age guidance, not curriculum certification