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

2021
Views:

321

Pages:

1
Author:

5CelestialChronicle

Advanced Math Vectors Unit Vectors and v Find the unit vector in the direction of v by dividing each component of v by the magnitude of v. 1. v = (-3, -4) magnitude = √((-3)² + (-4)²) = 5 <-3/5, -4/5> 2. v = (8, -15) magnitude = √(8² + (-15)²) = 17 <8/17, -15/17> 3. v = <-9, 40> magnitude = √((-9)² + 40²) = 41 <-9/41, 40/41> Given v = 3i - 2j and u = -2i + 3j, find the following: 4. 2u + 3v 2u = -4i + 6j 3v = 9i - 6j -4i + 6j + 9i - 6j 5i + 0j 5i 5. -5u -5(-2i + 3j) 10i - 15j 6. v - 3u 3i - 2j - (-6i + 9j) 3i - 2j + 6i - 9j 9i - 11j 7. ||v|| √(3² + (-2)²) = √13 ≈ 3.6 8. ||u|| √((-2)² + 3²) = √13 ≈ 3.6 9. u + 2v -2i + 3j + 6i - 4j 4i - j 10. ||u + 2v|| u + 2v = 4i - j √(4² + (-1)²) = √17 ≈ 4.1 11. ||u - v|| u - v = -2i + 3j - (3i - 2j) = -2i + 3j - 3i + 2j = -5i + 5j √((-5)² + 5²) = √50 ≈ 7.1 12. 1/2u - 1/2v 1/2u = -i + 1.5j 1/2v = 1.5i - j 1.5i - j - (-i + 1.5j) 1.5i - j + i - 1.5j 2.5i - 2.5j