(15 pts) For A =2 3 4 5, B =3 −4 −3 5, a =< 3,7,−4...
(15 pts) For A =2 3 4 5, B =3 −4 −3 5, a =< 3,7,−4 >, b =< 4,1,−2 >, computethe following a) 2A−B b) 2a−b c) BT d) kak e) a·b f) A−1 g) the angle between a and b h) a unit vector in the direction of a
Homework Answers
7. Let 7 = (1,-1,-2), ū = (2,-1,1) and = (2,-2,-4). Find: (a) *(-20) (4 pts)...
7. Let 7 = (1,-1,-2), ū = (2,-1,1) and = (2,-2,-4). Find: (a) *(-20) (4 pts) (b) (+37). ū (4 pts) (c) The vector of magnitude 5 that points in the same direction as (4 pts). (d) The angle between 7 and ū (4 pts). (e) Find Projz() (4 pts).
manitudle of a Vector 5. Reter to Problem 4. Find the following B, e) the scalar...
manitudle of a Vector 5. Reter to Problem 4. Find the following B, e) the scalar product f)內, g) 3 * a) the scalar product b) the magnitude of A, x c) the magnitude of d) the angle between A and B, h) the angle between亡and T 4. Graph the following vectors on the same coordinate system (three dimensions) = -51 + 4)-6k 4. Given the vectors: 궂. 4个.价. Find the following a) A +
Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5,...
Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5, 9(-1,2,-4)-2, 9u(-1,2,-4) -3, and 9.(-1,2,-4) 6 Answer the following questions, and carefully justify all your answers. (a) Estimate the value of g(-0.8,2.1,-4.2). near y (b) In what direction from the point (-1,2, -4) does g decrease the fastest? What is the rate of change in this direction? (c) Which of the following objects exist(s)? Justify your answers, and find an equation for the ones...
Reter to Problem 4. Find the following a) the scalar product A, b) the magnitude of...
Reter to Problem 4. Find the following a) the scalar product A, b) the magnitude of A, c) the magnitude of Ề, d) the angle between A and 5. e) the scalar productでD ICI g) 31 h) the angle between andT 6. Given the vectors: a-介-31 + k, b -- 1 + j Find the following a) A vector such that a bo, b) A vector a such that 2 a 3. d o, c) the magnitude of , e)...
2 pts Question 5 If 8, is 61.7 degrees and 82 is 103.7 degrees, what angle...
2 pts Question 5 If 8, is 61.7 degrees and 82 is 103.7 degrees, what angle in degrees is made between the vertically hanging load and the boom? DIL DO E7 3 4 6 7 8 E R T Y U D F G H J o N (O R LO LL
2 pts Question 5 If 8, is 61.7 degrees and 82 is 103.7 degrees, what angle in degrees is made between the vertically hanging load and the boom?...
Free Response (15 pts 1 Two long parallel wires carry aarrents I:= 5 4 and 1;=3...
Free Response (15 pts 1 Two long parallel wires carry aarrents I:= 5 4 and 1;=3 4 in the directions shown in the figure. Take d= 0.20 m. (us! = 42 * 10 T mA -----.. a) Find the magnetic field at a point midway between the wires. Express you answer in unit vector notation. (9 pts) d- b) Find the magnetic field at point P, located above the wire carrying the 3 A current. Express your answer in unit...
(b) Let F, G and H be the following sets of ordered pairs F {(1,1), (2,...
(b) Let F, G and H be the following sets of ordered pairs F {(1,1), (2, 2), (3,7), (4,1)} G {(1,1), (2, 1) (3, 2), (3,3), (4,2)} н 3 {(1,1), (2, 3), (3, 4), (4, 2)} (i) Does F define a function f :{1,2,3,4} (ii) Does G define a function g : {1,2,3,4} (iї) Does H define a function h : {1,2,3,4} —> {1, 2, 3, 4}? (iv) For those of f, g and h that are functions, write down...
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the...
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
2 1 3 4 1 -1 2 5. Suppose A= b and Adet(A) = 5. What...
2 1 3 4 1 -1 2 5. Suppose A= b and Adet(A) = 5. What are the values of the C a ef g h) following determinants? [3 marks] 4 3 1 2 -1 2 1 a. 2e 2f 2g 2h d b c 4 3 2 1 3 2 -1 b. c+2x d+3x b-x a+x h f 3 4 5 -1 2 3 -2 C. d a+3b C g h e+3f f Page 5 SPRING 2019 ASSIGNMENT FILE...
Consider the following graph: b a 15 5 10 3 e 6 d 30 C 5...
Consider the following graph: b a 15 5 10 3 e 6 d 30 C 5 6 2 i j h f 4 k (c) (4 pts.) Show all the articulation points in the graph if exist
7. Let 7 = (1,-1,-2), ū = (2,-1,1) and = (2,-2,-4). Find: (a) *(-20) (4 pts) (b) (+37). ū (4 pts) (c) The vector of magnitude 5 that points in the same direction as (4 pts). (d) The angle between 7 and ū (4 pts). (e) Find Projz() (4 pts).
manitudle of a Vector 5. Reter to Problem 4. Find the following B, e) the scalar product f)內, g) 3 * a) the scalar product b) the magnitude of A, x c) the magnitude of d) the angle between A and B, h) the angle between亡and T 4. Graph the following vectors on the same coordinate system (three dimensions) = -51 + 4)-6k 4. Given the vectors: 궂. 4个.价. Find the following a) A +
Problem 2. Suppose that gx, y, 2) is a function with the following properties: -1,2,-4 5, 9(-1,2,-4)-2, 9u(-1,2,-4) -3, and 9.(-1,2,-4) 6 Answer the following questions, and carefully justify all your answers. (a) Estimate the value of g(-0.8,2.1,-4.2). near y (b) In what direction from the point (-1,2, -4) does g decrease the fastest? What is the rate of change in this direction? (c) Which of the following objects exist(s)? Justify your answers, and find an equation for the ones...
Reter to Problem 4. Find the following a) the scalar product A, b) the magnitude of A, c) the magnitude of Ề, d) the angle between A and 5. e) the scalar productでD ICI g) 31 h) the angle between andT 6. Given the vectors: a-介-31 + k, b -- 1 + j Find the following a) A vector such that a bo, b) A vector a such that 2 a 3. d o, c) the magnitude of , e)...
2 pts Question 5 If 8, is 61.7 degrees and 82 is 103.7 degrees, what angle in degrees is made between the vertically hanging load and the boom? DIL DO E7 3 4 6 7 8 E R T Y U D F G H J o N (O R LO LL
2 pts Question 5 If 8, is 61.7 degrees and 82 is 103.7 degrees, what angle in degrees is made between the vertically hanging load and the boom?...
Free Response (15 pts 1 Two long parallel wires carry aarrents I:= 5 4 and 1;=3 4 in the directions shown in the figure. Take d= 0.20 m. (us! = 42 * 10 T mA -----.. a) Find the magnetic field at a point midway between the wires. Express you answer in unit vector notation. (9 pts) d- b) Find the magnetic field at point P, located above the wire carrying the 3 A current. Express your answer in unit...
(b) Let F, G and H be the following sets of ordered pairs F {(1,1), (2, 2), (3,7), (4,1)} G {(1,1), (2, 1) (3, 2), (3,3), (4,2)} н 3 {(1,1), (2, 3), (3, 4), (4, 2)} (i) Does F define a function f :{1,2,3,4} (ii) Does G define a function g : {1,2,3,4} (iї) Does H define a function h : {1,2,3,4} —> {1, 2, 3, 4}? (iv) For those of f, g and h that are functions, write down...
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
2 1 3 4 1 -1 2 5. Suppose A= b and Adet(A) = 5. What are the values of the C a ef g h) following determinants? [3 marks] 4 3 1 2 -1 2 1 a. 2e 2f 2g 2h d b c 4 3 2 1 3 2 -1 b. c+2x d+3x b-x a+x h f 3 4 5 -1 2 3 -2 C. d a+3b C g h e+3f f Page 5 SPRING 2019 ASSIGNMENT FILE...
Consider the following graph: b a 15 5 10 3 e 6 d 30 C 5 6 2 i j h f 4 k (c) (4 pts.) Show all the articulation points in the graph if exist
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