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, 15).
8 · 15 · 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 = (63, 60).
63 · 60 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (75, 40).
75 · 40 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (20, 15).
20 · 15 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (20, 21).
20 · 21 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (84, 80).
84 · 80 · 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 = (96, 28).
96 · 28 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (35, 120).
35 · 120 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (80, 84).
80 · 84 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (36, 15).
36 · 15 · 2D vector magnitude

12 questions · Seed 44 · 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, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
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 = (63, 60).
87
|v| = √(63² + 60²) = √(3969 + 3600) = √7569 = 87.
4. Find the magnitude |v| of the vector v = (75, 40).
85
|v| = √(75² + 40²) = √(5625 + 1600) = √7225 = 85.
5. Find the magnitude |v| of the vector v = (20, 15).
25
|v| = √(20² + 15²) = √(400 + 225) = √625 = 25.
6. Find the magnitude |v| of the vector v = (20, 21).
29
|v| = √(20² + 21²) = √(400 + 441) = √841 = 29.
7. Find the magnitude |v| of the vector v = (84, 80).
116
|v| = √(84² + 80²) = √(7056 + 6400) = √13456 = 116.
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 = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.
10. Find the magnitude |v| of the vector v = (35, 120).
125
|v| = √(35² + 120²) = √(1225 + 14400) = √15625 = 125.
11. Find the magnitude |v| of the vector v = (80, 84).
116
|v| = √(80² + 84²) = √(6400 + 7056) = √13456 = 116.
12. Find the magnitude |v| of the vector v = (36, 15).
39
|v| = √(36² + 15²) = √(1296 + 225) = √1521 = 39.

12 questions · Seed 44 · 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, 15).
8 · 15 · 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 = (63, 60).
63 · 60 · 2D vector magnitude
4. Find the magnitude |v| of the vector v = (75, 40).
75 · 40 · 2D vector magnitude
5. Find the magnitude |v| of the vector v = (20, 15).
20 · 15 · 2D vector magnitude
6. Find the magnitude |v| of the vector v = (20, 21).
20 · 21 · 2D vector magnitude
7. Find the magnitude |v| of the vector v = (84, 80).
84 · 80 · 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 = (96, 28).
96 · 28 · 2D vector magnitude
10. Find the magnitude |v| of the vector v = (35, 120).
35 · 120 · 2D vector magnitude
11. Find the magnitude |v| of the vector v = (80, 84).
80 · 84 · 2D vector magnitude
12. Find the magnitude |v| of the vector v = (36, 15).
36 · 15 · 2D vector magnitude

12 questions · Seed 44 · 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, 15).
17
|v| = √(8² + 15²) = √(64 + 225) = √289 = 17.
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 = (63, 60).
87
|v| = √(63² + 60²) = √(3969 + 3600) = √7569 = 87.
4. Find the magnitude |v| of the vector v = (75, 40).
85
|v| = √(75² + 40²) = √(5625 + 1600) = √7225 = 85.
5. Find the magnitude |v| of the vector v = (20, 15).
25
|v| = √(20² + 15²) = √(400 + 225) = √625 = 25.
6. Find the magnitude |v| of the vector v = (20, 21).
29
|v| = √(20² + 21²) = √(400 + 441) = √841 = 29.
7. Find the magnitude |v| of the vector v = (84, 80).
116
|v| = √(84² + 80²) = √(7056 + 6400) = √13456 = 116.
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 = (96, 28).
100
|v| = √(96² + 28²) = √(9216 + 784) = √10000 = 100.
10. Find the magnitude |v| of the vector v = (35, 120).
125
|v| = √(35² + 120²) = √(1225 + 14400) = √15625 = 125.
11. Find the magnitude |v| of the vector v = (80, 84).
116
|v| = √(80² + 84²) = √(6400 + 7056) = √13456 = 116.
12. Find the magnitude |v| of the vector v = (36, 15).
39
|v| = √(36² + 15²) = √(1296 + 225) = √1521 = 39.

12 questions · Seed 44 · Age guidance, not curriculum certification