University:
University of North Georgia
Course:
MATH 1113 | Precalculus
Academic year:

2021
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409

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5
Author:

larbiwxcvbn

Advanced Math Vectors Quiz Review Name: Section 7.3 Draw the vector from 𝑷𝟏 to 𝑷𝟐 . Then, find the vector in component form with the initial point 𝑷𝟏 and terminal point 𝑷𝟐 . Finally, draw the vector in component form. 1. 𝑃1 (−8, 2) and 𝑃2 (−3, 5) 2. 𝑃1 (6, −4) and 𝑃2 (1, −7) 1.)_______________ 2.)_______________ Find the magnitude and direction for the given vector. Draw the vector to help decide the direction! Estimate the magnitude to the nearest tenth. Estimate the direction to the nearest tenth of a degree. 3. 𝒗 = 〈−5, 12〉 4. 𝒗 = 〈3, 6〉 3.)_______________ Magnitude 3.)_______________ Direction 4.)_______________ Magnitude 4.)_______________ Direction 1 Find the magnitude and direction for the given vector. Draw the vector to help decide the direction! Estimate the magnitude to the nearest tenth. Estimate the direction to the nearest tenth of a degree. 5. 𝒗 = 〈6, −8〉 6. 𝒗 = 〈−2, −7〉 5.)_______________ Magnitude 5.)_______________ Direction 6.)_______________ Magnitude 6.)_______________ Direction Given 𝒖 = 〈−𝟑, 𝟖〉, 𝒗 = 〈−𝟐, −𝟓〉 and 𝒘 = 〈𝟎, 𝟔〉 7. ‖𝒖‖ 8. ‖𝒗‖ 9. ‖𝒘‖ 7.)_______________ 8.)_______________ 9.)_______________ 10. ‖𝒖 + 𝒗‖ 11. ‖𝒗 + 2𝒖‖ 12. −4𝒗 10.)______________ 11.)______________ 12.)______________ 2 Given 𝒖 = 〈−𝟑, 𝟖〉, 𝒗 = 〈−𝟐, −𝟓〉 and 𝒘 = 〈𝟎, 𝟔〉 13. 2𝒘 − 3𝒗 14. 1 𝒘 2 15. ‖3𝒘 − 4𝒗‖ + 5𝒖 13.)______________ 14.)______________ 15.)______________ Find the unit vector in the direction 𝒗 of by dividing each component of 𝒗 by the magnitude of 𝒗. 16. 𝒗 = 〈−8, −15〉 17. 𝒗 = 〈12, −16〉 16.)______________ 17.)______________ Given 𝒗 = 𝟐𝒊 − 𝟒𝒋 and 𝒖 = −𝒊 + 𝟓𝒋, find the following: 18. 4𝒖 − 5𝒗 19. 3𝒗 − 𝒖 18.)______________ 19.)______________ 20. ‖𝒗‖ 21. ‖𝒖‖ 20.)______________ 21.)______________ 22. ‖𝒖 + 𝟐𝒗‖ 23. 1 𝒗 2 1 2 − 𝒖 22.)______________ 23.)______________ 3 Draw vectors 𝒖 and 𝒗 on the same coordinate plane. Then, find the dot product of 𝒖 and 𝒗, ‖𝒖‖ and ‖𝒗‖. Finally, find the measure of the angle between the two vectors. 24. 𝒖 = 〈−5, 7〉 and 𝒗 = 〈−2, 1〉 𝒖 ∙𝒗= ‖𝒖‖ = ‖𝒗‖ = Angle between the two vectors = ___________ 25. 𝒖 = 〈8, −8〉 and 𝒗 = 〈2, 3〉 𝒖 ∙𝒗= ‖𝒖‖ = ‖𝒗‖ = Angle between the two vectors = ___________ 26. 𝒖 = 〈2, −4〉 and 𝒗 = 〈10, 5〉 𝒖 ∙𝒗= ‖𝒖‖ = ‖𝒗‖ = Angle between the two vectors = ___________ 4 Draw vectors 𝒖 and 𝒗 on the same coordinate plane. Then, find the dot product of 𝒖 and 𝒗, ‖𝒖‖ and ‖𝒗‖. Finally, find the measure of the angle between the two vectors. 27. 𝒖 = 2𝒊 − 2𝒋 and 𝒗 = 3𝒊 + 3𝒋 𝒖 ∙𝒗= ‖𝒖‖ = ‖𝒗‖ = Angle between the two vectors = ___________ 28. 𝒖 = −6𝒊 + 7𝒋 and 𝒗 = −𝒊 − 2𝒋 𝒖 ∙𝒗= ‖𝒖‖ = ‖𝒗‖ = Angle between the two vectors = ___________ 29. 𝒖 = 6𝒊 + 4𝒋 and 𝒗 = −𝒊 + 3𝒋 𝒖 ∙𝒗= ‖𝒖‖ = ‖𝒗‖ = Angle between the two vectors = ___________ 5

Math Vectors Quiz Review

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