Sec. 12.2 Enhanced Assignment

Instructor: Shijun Zheng Course: Spring 2023 - Calculus III (MATH2243-A-B) Student: Jalen Wilson Date: 07/11/24 Assignment: Sec. 12.2 Enhanced Assign 1. Let u = 4, − 7 . Find the component form and magnitude​(length) of the vector 3u. The component form is 3u = ​(Simplify your​answers.) 12 , − 21 . The magnitude is 3u = 3 65 . ​(Type an exact​answer, using radicals as needed.) 2. For u = 7, − 3 and v = − 2, − 5 ​, find the component form and the magnitude of u + v. u+v= 5 , ​(Simplify your​answers.) u+v = −8 89 ​(Type an exact​answer, using radicals as needed.) 3. Let u = 2, − 4 and v = − 1,2 . Find the component form and magnitude​(length) of the vector 4u − 5v. The component form is 4u − 5v = ​(Simplify your​answers.) The magnitude is 4u − 5v = 13 , − 26 . 13 5 ​(Type an exact​answer, using radicals as needed.) 4. Find the component form of the vector PQ​, where P = (3,1) and Q = (8, − 9). The component form of PQ is ​(Simplify your​answers.) 5 , − 10 . 5. Express the vector P P in the form v = v i + v j + v k if P is the point (2,1,2) and P is the point (9,5,8). 1 2 1 2 3 1 2 P1 P2 = 7 i+ 4 j+ 6 k ​(Simplify your​answers.) 6. Express the following vector in the form v = v1 i + v2 j + v3 k. 3u − v if u = 〈7,1​, − 9〉 and v = 〈3​, − 1​,2〉 3u − v = 18 ​(Simplify your​answers.) i+ 4 j+ − 29 k 7. Copy vectors u​, v​, and w head to tail as needed to sketch the indicated vectors. a. u + v b. u + v + w c. u − v d. u − w u w v Choose the correct sketch for u + v. A. B. C. D. C. D. C. D. C. D. Choose the correct sketch for u + v + w. A. B. Choose the correct sketch for u − v. A. B. Choose the correct sketch for u − w. A. B. 8. Express the vector − 5 k as a product of its length and direction. −5k= 5 0 i+ 0 j+ −1 (​ Simplify your answers. Use integers or fractions for any numbers in the​expression.) 9. 2 Estimate the error if cos t is approximated by 1 − The error is approximately 0.00011 t 4 2 + t 1 8 4! in the integral ∫ cos t2 dt. 0 . ​(Round to five decimal places as​needed.) k 10. Find the vertices and foci for the ellipse. Graph the equation. x 2 64 2 + y 25 =1 What are the coordinates of the​vertices? (8,0),( − 8,0) (​ Type an ordered pair. Type exact answers for each​coordinate, using radicals as needed. Use a comma to separate answers as​needed.) What are the coordinates of the​foci? 39 ,0 , − 39 ,0 (​ Type an ordered pair. Type exact answers for each​coordinate, using radicals as needed. Use a comma to separate answers as​needed.) Which graph shown below is the graph of the​ellipse? A. B. 10 y C. 10 x -10 10 -10 y D. 10 x -10 10 -10 y 10 x -10 10 -10 y x -10 10 -10