Free Printable WorksheetMathTrigonometryMath CurriculumUTRI.TA.3

TRIG.122 Add, subtract, and scale vectors to model resultant quantities Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Trigonometry Math worksheet provides structured practice on TRIG.122 Add, subtract, and scale vectors to model resultant quantities. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

TRIG.122 Add, subtract, and scale vectors to model resultant quantities - Primary standard selected for prompt fields in this prompt cell: UTRI.TA.3. Skill statement in this prompt cell: Select the resultant vector from addition, subtraction, or scaling and identify the correct magnitude and direction interpretation. Associated standards listed with this skill in this prompt cell: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Trigonometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related TRIG.122 Add, subtract, and scale vectors to model resultant quantities skill assessments:

Problem 1Difficulty: Mastery

Points A(1, 1), B(9, 7), C(0, -3), D(-2, 1), E(4, 4), and F(5, -1) define AB, CD, and EF. Which option gives 0.5(AB + CD) - 2EF? Select the option with the correct resultant vector, magnitude, and direction.

Aresultant vector = <5, -5>; magnitude = sqrt(50); direction = about 45 degrees south of east

Bresultant vector = <6, 10>; magnitude = sqrt(136); direction = about 59 degrees north of east

Cresultant vector = <1, -15>; magnitude = sqrt(226); direction = about 86.2 degrees south of east

Dresultant vector = <1, 15>; magnitude = sqrt(226); direction = about 86.2 degrees north of east

Solution & Explanation:First find AB = <8, 6>, CD = <-2, 4>, and EF = <1, -5>. Compute component by component: 0.5AB = <4, 3>; 0.5CD = <-1, 2>; -2EF = <-2, 10>, so the resultant is <1, 15>. Its magnitude is sqrt(226), and its direction is about 86.2 degrees north of east.

Problem 2Difficulty: Mastery

A navigation vector is computed from -3route1 + 2route2 + route3, with route1 = <4, -2>, route2 = <7, 5>, and route3 = <-1, -8>. Which option gives the resultant? Select the option with the correct resultant vector, magnitude, and direction.

Aresultant vector = <3, 24>; magnitude = sqrt(585); direction = about 82.9 degrees north of east

Bresultant vector = <25, -4>; magnitude = sqrt(641); direction = about 9.1 degrees south of east

Cresultant vector = <1, 8>; magnitude = sqrt(65); direction = about 82.9 degrees north of east

Dresultant vector = <11, 3>; magnitude = sqrt(130); direction = about 15.3 degrees north of east

Solution & Explanation:Compute component by component: -3route1 = <-12, 6>; 2route2 = <14, 10>; route3 = <-1, -8>, so the resultant is <1, 8>. Its magnitude is sqrt(65), and its direction is about 82.9 degrees north of east.

Problem 3Difficulty: Mastery

Points P(-2, 5), Q(4, 3), R(1, -1), S(0, 4), T(3, 3), and U(5, 0) define vectors PQ, RS, and TU. Which option gives 2PQ - RS - 3TU? Select the option with the correct resultant vector, magnitude, and direction.

Aresultant vector = <19, -18>; magnitude = sqrt(685); direction = about 43.5 degrees south of east

Bresultant vector = <7, 0>; magnitude = 7; direction = due east

Cresultant vector = <17, -8>; magnitude = sqrt(353); direction = about 25.2 degrees south of east

Dresultant vector = <5, 3>; magnitude = sqrt(34); direction = about 31 degrees north of east

Solution & Explanation:First find PQ = <6, -2>, RS = <-1, 5>, and TU = <2, -3>. Compute component by component: 2PQ = <12, -4>; -RS = <1, -5>; -3TU = <-6, 9>, so the resultant is <7, 0>. Its magnitude is 7, and its direction is due east.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Trigonometry Math students. It aligns with educational standard UTRI.TA.3 (Primary standard selected for prompt fields in this prompt cell: UTRI.TA.3. Skill statement in this prompt cell: Select the resultant vector from addition, subtraction, or scaling and identify the correct magnitude and direction interpretation. Associated standards listed with this skill in this prompt cell: UTRI.TA.3; TEKS §111.42(c)(4)(I)-(K); CCSS HSN.VM (if adopted). Use this prompt-provided wording as the supporting standard description for this workflow.).