This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: pasha (sep635) HW#11 Antoniewicz (56445) 1 This printout should have 36 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 (part 1 of 5) 2.0 points Consider vectors ~ A and ~ B such that ~ A = h 200 , 200 , 300 i and ~ B = h 300 , 500 , 300 i . Find ~ A + ~ B . 1. h 100 , 300 , i correct 2. h 100 , 200 , 100 i 3. h 200 , 100 , 200 i 4. h 300 , , 100 i 5. h 200 , 300 , 200 i Explanation: To add vectors, we add respective compo nents: A x + B x = 200 + ( 300) = 100 , A y + B y = 200 + 500 = 300 , and A z + B z = 300 + 300 = 0 , so ~ A + ~ B = h A x + B x , A y + B y , A z + B z i = h 100 , 300 , i . 002 (part 2 of 5) 2.0 points Find ~ A + ~ B . Correct answer: 316 . 228. Explanation: The magnitude of ~ A + ~ B is ~ A + ~ B = q ( A x + B x ) 2 +( A y + B y ) 2 +( A z + B z ) 2 = q ( 100) 2 + (300) 2 + (0) 2 = 316 . 228 . 003 (part 3 of 5) 2.0 points Find ~ A . Correct answer: 412 . 311. Explanation: We follow the same procedure as for the previous part of the problem. ~ A = q A 2 x + A 2 y + A 2 z = q (200) 2 + ( 200) 2 + ( 300) 2 = 412 . 311 . 004 (part 4 of 5) 2.0 points Find ~ B . Correct answer: 655 . 744. Explanation: We follow the same procedure again. ~ B = q B 2 x + B 2 y + B 2 z = q ( 300) 2 + (500) 2 + (300) 2 = 655 . 744 . 005 (part 5 of 5) 2.0 points Find ~ A + ~ B . Correct answer: 1068 . 05. Explanation: Here we simply add the values we obtained in parts 3 and 4: ~ A + ~ B = 412 . 311 + 655 . 744 = 1068 . 05 . 006 10.0 points Consider the following figure: pasha (sep635) HW#11 Antoniewicz (56445) 2 ~ t ~ r ~ s Which of the following statements about the three vectors in the figure are correct? List all that apply, separated by commas. A ~ s = ~ t ~ r B ~ r = ~ t ~ s C ~ r + ~ t = ~ s D ~ s + ~ t = ~ r E ~ r + ~ s = ~ t Correct answer: A, B, E. Explanation: Vector subtraction can be tricky. Just as one way to subtract scalar quantities is to add the negative of the number being subtracted ( i.e. , instead of 5 3 = 2 we could write 5 + ( 3) = 2), we can do the same with vectors. We start by writing down the first vector. For option A , the first vector in the subtraction is ~ t , so we draw it: ~ t Then, we add the negative of the vector being subtracted. When we write down ~ r , it will be pointing in the opposite direction from ~ r . We place ~ r s starting point at the tip of ~ t , and from here, we are simply adding vectors: ~ t ~ s ~ r Notice that the resultant vector, ~ s , is ex actly the same as the original ~ s in the figure we started with. So ~ t + ( ~ r ) = ~ t ~ r = ~ s, and option A is true. Following the same procedure for the re maining options, we can determine that A , B , and E are true statements, while the oth ers are false....
View
Full
Document
 Fall '08
 Turner

Click to edit the document details