University:
Florida Gateway College
Course:
MAC 2312 | Calculus II
Academic year:

2021
Views:

301

Pages:

5
Author:

StellarStrategist

Vectors Quiz Review Name: Key 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. P1(-8, 2) and P2(-3, 5) Vector: <5, 3> vector going from (8,2) to (3,5) P1(6, -4) and P2(1, -7) Vector: <-5, -3> vector going from (6,4) to (1,7) 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. 1 1. v = <-5, 12> Magnitude: |v| = √((-5)² + 12²) = 13 Direction: tan⁻¹(12/-5) ≈ -67.4° Reference angle: 67.4° Q2: 180° - 67.4° = 112.6° vector in the second quadrant v = <3, 6> Magnitude: |v| = √(3² + 6²) = 6.7 Direction: tan⁻¹(6/3) = 63.4° Q1: 63.4° vector in the first quadrant Given u = <3, 8>, v = <-2, -5> and w = <0, 6> 13. 2w - 3v 2w = <0, 12> 3v = <-6, -15> <0, 12> - <-6, -15> = <6, 27> 14. 1/2w + 5u 1/2w = <0, 3> 5u = <-15, 40> <0, 3> + <-15, 40> = <-15, 43> 15. ||3w - 4v|| 3w = <0, 18> 4v = <-8, -20> <0, 18> - <-8, -20> = <8, 38> √(8² + 38²) = 38.8 **Find the unit vector in the direction of v by dividing each component of v by the magnitude of v.** 16. v = <-8, -15> ||v|| = √((-8)² + (-15)²) = 17 <-8/17, -15/17> 17. v = <12, -16> ||v|| = √(12² + (-16)²) = 20 <12/20, -16/20> = <3/5, -4/5> **Given u = 2i - 4j and u = -i + 5j, find the following:** 18. 4u - 5v 4u = 8i - 16j 5v = -5i + 25j 8i - 16j - (-5i + 25j) = 13i - 41j 19. 3v - u 3v = 6i - 12j 6i - 12j - (-i + 5j) = 7i - 17j 20. ||u|| √(2² + (-4)²) = √20 = 4.5 21. ||v|| √((-1)² + 5²) = √26 = 5.1 22. ||u + 2v|| 2v = 4i - 8j u + 2v = -i + 5j + 4i - 8j = 3i - 3j √(3² + (-3)²) = 4.2 23. ||(1/2)u - (1/2)v|| 1/2u = 1/2i - 2j 1/2v = -1/2i + 5/2j 1/2i - 2j - (-1/2i + 5/2j) = 3/2i - 9/2j √((3/2)² + (-9/2)²) = 4.2 **24. u = (-5, 7) and v = (-2, 1)** [Image of vectors u and v on a coordinate plane] u · v = (-5)(-2) + (7)(1) = 17 ||u|| = √((-5)² + 7²) = 8.6 ||v|| = √((-2)² + 1²) = 2.2 Angle between the two vectors = 26.0° **25. u = (8, -8) and v = (2, 3)** [Image of vectors u and v on a coordinate plane] u · v = (8)(2) + (-8)(3) = -8 ||u|| = √(8² + (-8)²) = 11.3 ||v|| = √(2² + 3²) = 3.6 Angle between the two vectors = 101.3° **26. u = (2, -4) and v = (10, 5)** [Image of vectors u and v on a coordinate plane] u · v = (2)(10) + (-4)(5) = 0 ||u|| = √(2² + (-4)²) = 4.5 ||v|| = √(10² + 5²) = 11.2 Angle between the two vectors = 90°

Math Vectors Quiz Review Key

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