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Grade 12 Vectors Worksheet with Answers

Grade 12 (US) · Year 13 (UK) · Class 12 (India) · Math

Unit 2: Vectors & MatricesVectorsCCSS N-VM.A.1

Vector addition, scalar multiples, magnitude and the dot product. This free high school worksheet has 12 questions and a full answer key. Print it or save it as a PDF — every answer is checked by code, not guessed.

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Vectors

Grade 12 · Math

Score___ / 12

Name

Class

Date

Learning goal: Vectors · CCSS N-VM.A.1

Directions: Use the pictures to help you. Solve each problem. Show your work, then write your answer in the box.

Example

u = <1, 7>. Find 3u.

Answer: <3, 21>

RememberMatrices and vectors

123456=1·5 + 2·6 = 173·5 + 4·6 = 39Row × column, then add.det [a b; c d] = ad − bcx = 4y = 3|v| = 5v = ⟨4, 3⟩|v| = √(x² + y²)add: tip to tail
  1. 1

    Find the magnitude of <-5, 12>.

    Answer
  2. 2

    u = <-3, -2>, v = <1, 5>. Find u + v.

    xyuv
    Answer
  3. 3

    Find the magnitude of <-3, 4>.

    Answer
  4. 4

    u = <5, 5>, v = <-1, -6>. Find u + v.

    xyuv
    Answer
  5. 5

    u = <5, -5>, v = <3, 4>. Find u - v.

    xyuv
    Answer
  6. 6

    Find the magnitude of <7, 24>.

    Answer
  7. 7

    u = <8, 8>, v = <5, 5>. Find u - v.

    xyuv
    Answer
  8. 8

    Find the dot product of <-9, -9> and <2, -8>.

    Answer
  9. 9

    u = <5, -9>, v = <7, 7>. Find u - v.

    xyuv
    Answer
  10. 10

    u = <-9, -8>, v = <-2, -1>. Find u + v.

    xyuv
    Answer
  11. 11

    u = <0, -1>, v = <-8, 2>. Find u - v.

    xyuv
    Answer
  12. 12

    Find the magnitude of <-7, 24>.

    Answer

★ Challenge corner for fast finishers

11 points are marked on a circle. How many different triangles can be drawn using these points as corners?

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Teacher's comments

Free printable worksheets with answer keys · aethelsystems.com/worksheets/math/12/vectors

Answer key (click to show)
  1. 1.13
  2. 2.<-2, 3>
  3. 3.5
  4. 4.<4, -1>
  5. 5.<2, -9>
  6. 6.25
  7. 7.<3, 3>
  8. 8.54
  9. 9.<-2, -16>
  10. 10.<-11, -9>
  11. 11.<8, -3>
  12. 12.25
  13. ★165 (challenge corner)

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