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 = (9, 40).
9 · 40 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (24, 45).
24 · 45 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (36, 160).
36 · 160 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (9, 12).
9 · 12 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (60, 25).
60 · 25 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (60, 63).
60 · 63 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (96, 28).
96 · 28 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (15, 20).
15 · 20 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (24, 10).
24 · 10 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (12, 9).
12 · 9 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (40, 42).
40 · 42 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (20, 48).
20 · 48 · 2D vector magnitude

12 questions · Seed 48 · 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 = (9, 40).
41
|v| = √(9² + 40²) = √(81 + 1600) = √1681 = 41.
2. Find the magnitude |v| of the vector v = (24, 45).
51
|v| = √(24² + 45²) = √(576 + 2025) = √2601 = 51.
3. Find the magnitude |v| of the vector v = (36, 160).
164
|v| = √(36² + 160²) = √(1296 + 25600) = √26896 = 164.
4. Find the magnitude |v| of the vector v = (9, 12).
15
|v| = √(9² + 12²) = √(81 + 144) = √225 = 15.
5. Find the magnitude |v| of the vector v = (60, 25).
65
|v| = √(60² + 25²) = √(3600 + 625) = √4225 = 65.
6. Find the magnitude |v| of the vector v = (60, 63).
87
|v| = √(60² + 63²) = √(3600 + 3969) = √7569 = 87.
7. Find the magnitude |v| of the vector v = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.
8. Find the magnitude |v| of the vector v = (15, 20).
25
|v| = √(15² + 20²) = √(225 + 400) = √625 = 25.
9. Find the magnitude |v| of the vector v = (24, 10).
26
|v| = √(24² + 10²) = √(576 + 100) = √676 = 26.
10. Find the magnitude |v| of the vector v = (12, 9).
15
|v| = √(12² + 9²) = √(144 + 81) = √225 = 15.
11. Find the magnitude |v| of the vector v = (40, 42).
58
|v| = √(40² + 42²) = √(1600 + 1764) = √3364 = 58.
12. Find the magnitude |v| of the vector v = (20, 48).
52
|v| = √(20² + 48²) = √(400 + 2304) = √2704 = 52.

12 questions · Seed 48 · 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 = (9, 40).
9 · 40 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (24, 45).
24 · 45 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (36, 160).
36 · 160 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (9, 12).
9 · 12 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (60, 25).
60 · 25 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (60, 63).
60 · 63 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (96, 28).
96 · 28 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (15, 20).
15 · 20 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (24, 10).
24 · 10 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (12, 9).
12 · 9 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (40, 42).
40 · 42 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (20, 48).
20 · 48 · 2D vector magnitude

12 questions · Seed 48 · 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 = (9, 40).
41
|v| = √(9² + 40²) = √(81 + 1600) = √1681 = 41.
2. Find the magnitude |v| of the vector v = (24, 45).
51
|v| = √(24² + 45²) = √(576 + 2025) = √2601 = 51.
3. Find the magnitude |v| of the vector v = (36, 160).
164
|v| = √(36² + 160²) = √(1296 + 25600) = √26896 = 164.
4. Find the magnitude |v| of the vector v = (9, 12).
15
|v| = √(9² + 12²) = √(81 + 144) = √225 = 15.
5. Find the magnitude |v| of the vector v = (60, 25).
65
|v| = √(60² + 25²) = √(3600 + 625) = √4225 = 65.
6. Find the magnitude |v| of the vector v = (60, 63).
87
|v| = √(60² + 63²) = √(3600 + 3969) = √7569 = 87.
7. Find the magnitude |v| of the vector v = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.
8. Find the magnitude |v| of the vector v = (15, 20).
25
|v| = √(15² + 20²) = √(225 + 400) = √625 = 25.
9. Find the magnitude |v| of the vector v = (24, 10).
26
|v| = √(24² + 10²) = √(576 + 100) = √676 = 26.
10. Find the magnitude |v| of the vector v = (12, 9).
15
|v| = √(12² + 9²) = √(144 + 81) = √225 = 15.
11. Find the magnitude |v| of the vector v = (40, 42).
58
|v| = √(40² + 42²) = √(1600 + 1764) = √3364 = 58.
12. Find the magnitude |v| of the vector v = (20, 48).
52
|v| = √(20² + 48²) = √(400 + 2304) = √2704 = 52.

12 questions · Seed 48 · Age guidance, not curriculum certification