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 = (18, 80).
18 · 80 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (35, 120).
35 · 120 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (20, 21).
20 · 21 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (40, 75).
40 · 75 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (160, 36).
160 · 36 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (24, 10).
24 · 10 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (45, 200).
45 · 200 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (15, 8).
15 · 8 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (16, 12).
16 · 12 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (32, 60).
32 · 60 · 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 = (9, 12).
9 · 12 · 2D vector magnitude

12 questions · Seed 47 · 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 = (18, 80).
82
|v| = √(18² + 80²) = √(324 + 6400) = √6724 = 82.
2. Find the magnitude |v| of the vector v = (35, 120).
125
|v| = √(35² + 120²) = √(1225 + 14400) = √15625 = 125.
3. Find the magnitude |v| of the vector v = (20, 21).
29
|v| = √(20² + 21²) = √(400 + 441) = √841 = 29.
4. Find the magnitude |v| of the vector v = (40, 75).
85
|v| = √(40² + 75²) = √(1600 + 5625) = √7225 = 85.
5. Find the magnitude |v| of the vector v = (160, 36).
164
|v| = √(160² + 36²) = √(25600 + 1296) = √26896 = 164.
6. Find the magnitude |v| of the vector v = (24, 10).
26
|v| = √(24² + 10²) = √(576 + 100) = √676 = 26.
7. Find the magnitude |v| of the vector v = (45, 200).
205
|v| = √(45² + 200²) = √(2025 + 40000) = √42025 = 205.
8. Find the magnitude |v| of the vector v = (15, 8).
17
|v| = √(15² + 8²) = √(225 + 64) = √289 = 17.
9. Find the magnitude |v| of the vector v = (16, 12).
20
|v| = √(16² + 12²) = √(256 + 144) = √400 = 20.
10. Find the magnitude |v| of the vector v = (32, 60).
68
|v| = √(32² + 60²) = √(1024 + 3600) = √4624 = 68.
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 = (9, 12).
15
|v| = √(9² + 12²) = √(81 + 144) = √225 = 15.

12 questions · Seed 47 · 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 = (18, 80).
18 · 80 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (35, 120).
35 · 120 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (20, 21).
20 · 21 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (40, 75).
40 · 75 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (160, 36).
160 · 36 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (24, 10).
24 · 10 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (45, 200).
45 · 200 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (15, 8).
15 · 8 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (16, 12).
16 · 12 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (32, 60).
32 · 60 · 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 = (9, 12).
9 · 12 · 2D vector magnitude

12 questions · Seed 47 · 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 = (18, 80).
82
|v| = √(18² + 80²) = √(324 + 6400) = √6724 = 82.
2. Find the magnitude |v| of the vector v = (35, 120).
125
|v| = √(35² + 120²) = √(1225 + 14400) = √15625 = 125.
3. Find the magnitude |v| of the vector v = (20, 21).
29
|v| = √(20² + 21²) = √(400 + 441) = √841 = 29.
4. Find the magnitude |v| of the vector v = (40, 75).
85
|v| = √(40² + 75²) = √(1600 + 5625) = √7225 = 85.
5. Find the magnitude |v| of the vector v = (160, 36).
164
|v| = √(160² + 36²) = √(25600 + 1296) = √26896 = 164.
6. Find the magnitude |v| of the vector v = (24, 10).
26
|v| = √(24² + 10²) = √(576 + 100) = √676 = 26.
7. Find the magnitude |v| of the vector v = (45, 200).
205
|v| = √(45² + 200²) = √(2025 + 40000) = √42025 = 205.
8. Find the magnitude |v| of the vector v = (15, 8).
17
|v| = √(15² + 8²) = √(225 + 64) = √289 = 17.
9. Find the magnitude |v| of the vector v = (16, 12).
20
|v| = √(16² + 12²) = √(256 + 144) = √400 = 20.
10. Find the magnitude |v| of the vector v = (32, 60).
68
|v| = √(32² + 60²) = √(1024 + 3600) = √4624 = 68.
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 = (9, 12).
15
|v| = √(9² + 12²) = √(81 + 144) = √225 = 15.

12 questions · Seed 47 · Age guidance, not curriculum certification