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 = (8, 6).
8 · 6 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (36, 160).
36 · 160 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (48, 14).
48 · 14 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (24, 10).
24 · 10 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (24, 45).
24 · 45 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (9, 12).
9 · 12 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (60, 25).
60 · 25 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (40, 75).
40 · 75 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (8, 15).
8 · 15 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (27, 120).
27 · 120 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (45, 200).
45 · 200 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (105, 100).
105 · 100 · 2D vector magnitude

12 questions · Seed 43 · 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 = (8, 6).
10
|v| = √(8² + 6²) = √(64 + 36) = √100 = 10.
2. Find the magnitude |v| of the vector v = (36, 160).
164
|v| = √(36² + 160²) = √(1296 + 25600) = √26896 = 164.
3. Find the magnitude |v| of the vector v = (48, 14).
50
|v| = √(48² + 14²) = √(2304 + 196) = √2500 = 50.
4. Find the magnitude |v| of the vector v = (24, 10).
26
|v| = √(24² + 10²) = √(576 + 100) = √676 = 26.
5. Find the magnitude |v| of the vector v = (24, 45).
51
|v| = √(24² + 45²) = √(576 + 2025) = √2601 = 51.
6. Find the magnitude |v| of the vector v = (9, 12).
15
|v| = √(9² + 12²) = √(81 + 144) = √225 = 15.
7. Find the magnitude |v| of the vector v = (60, 25).
65
|v| = √(60² + 25²) = √(3600 + 625) = √4225 = 65.
8. Find the magnitude |v| of the vector v = (40, 75).
85
|v| = √(40² + 75²) = √(1600 + 5625) = √7225 = 85.
9. Find the magnitude |v| of the vector v = (8, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
10. Find the magnitude |v| of the vector v = (27, 120).
123
|v| = √(27² + 120²) = √(729 + 14400) = √15129 = 123.
11. Find the magnitude |v| of the vector v = (45, 200).
205
|v| = √(45² + 200²) = √(2025 + 40000) = √42025 = 205.
12. Find the magnitude |v| of the vector v = (105, 100).
145
|v| = √(105² + 100²) = √(11025 + 10000) = √21025 = 145.

12 questions · Seed 43 · 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 = (8, 6).
8 · 6 · 2D vector magnitude
2. Find the magnitude |v| of the vector v = (36, 160).
36 · 160 · 2D vector magnitude
3. Find the magnitude |v| of the vector v = (48, 14).
48 · 14 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (24, 10).
24 · 10 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (24, 45).
24 · 45 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (9, 12).
9 · 12 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (60, 25).
60 · 25 · 2D vector magnitude
8. Find the magnitude |v| of the vector v = (40, 75).
40 · 75 · 2D vector magnitude
9. Find the magnitude |v| of the vector v = (8, 15).
8 · 15 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (27, 120).
27 · 120 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (45, 200).
45 · 200 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (105, 100).
105 · 100 · 2D vector magnitude

12 questions · Seed 43 · 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 = (8, 6).
10
|v| = √(8² + 6²) = √(64 + 36) = √100 = 10.
2. Find the magnitude |v| of the vector v = (36, 160).
164
|v| = √(36² + 160²) = √(1296 + 25600) = √26896 = 164.
3. Find the magnitude |v| of the vector v = (48, 14).
50
|v| = √(48² + 14²) = √(2304 + 196) = √2500 = 50.
4. Find the magnitude |v| of the vector v = (24, 10).
26
|v| = √(24² + 10²) = √(576 + 100) = √676 = 26.
5. Find the magnitude |v| of the vector v = (24, 45).
51
|v| = √(24² + 45²) = √(576 + 2025) = √2601 = 51.
6. Find the magnitude |v| of the vector v = (9, 12).
15
|v| = √(9² + 12²) = √(81 + 144) = √225 = 15.
7. Find the magnitude |v| of the vector v = (60, 25).
65
|v| = √(60² + 25²) = √(3600 + 625) = √4225 = 65.
8. Find the magnitude |v| of the vector v = (40, 75).
85
|v| = √(40² + 75²) = √(1600 + 5625) = √7225 = 85.
9. Find the magnitude |v| of the vector v = (8, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
10. Find the magnitude |v| of the vector v = (27, 120).
123
|v| = √(27² + 120²) = √(729 + 14400) = √15129 = 123.
11. Find the magnitude |v| of the vector v = (45, 200).
205
|v| = √(45² + 200²) = √(2025 + 40000) = √42025 = 205.
12. Find the magnitude |v| of the vector v = (105, 100).
145
|v| = √(105² + 100²) = √(11025 + 10000) = √21025 = 145.

12 questions · Seed 43 · Age guidance, not curriculum certification