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![along u. (1) projection of u using the formula, I can) projection of u along [53] vai - 53 121 Aug](http://img.homeworklib.com/questions/8294cc60-f670-11eb-9340-2768d896d08b.png?x-oss-process=image/resize,w_560)
2. Let ū= (3,1, -7), ã = (1,0,5). (a) Find the vector component of u along...
2. Let ū= (3,1, -7), ã = (1,0,5). (a) Find the vector component of u along a. (b) Find the vector component of ü orthogonal to ä. (c) Find the angle between u and , in degrees.
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12...
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12 + 69, then find the following: A. 2w - 3ū B. ||2u - 57 C. v. W D. the angle between ü and v E. the direction angle of vector w F. (3 +70).ü G. a vector in the same direction as ū with magnitude of 12 H. a vector orthogonal to vector v with magnitude of 7 I. any vector that is orthogonal...
1. Let {ü, 7,w, i}, where u = (3,-2), v = (0,4), ū = (-1,5) and...
1. Let {ü, 7,w, i}, where u = (3,-2), v = (0,4), ū = (-1,5) and i = (-6,4). Find the components of the resultants obtained by doing the following linear combinations. a. r = 2ū - 40 b. š= 3ū – +20 +
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a...
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a unit vector in the opposite direction to ū. c) Find (ü.v)v. d) Find 11: e) Find the distance between ū and v. f) Are ū and y parallel, perpendicular, or neither? Explain. g) Verify the Triangle Inequality for ū and ū.
6-7. Given vectors U = -41 +12, V=51-2), W =-31 - 1 6. Find a) 3U...
6-7. Given vectors U = -41 +12, V=51-2), W =-31 - 1 6. Find a) 3U - 5V._b) 2V - WI 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculator ok)
6-7. Given vectors U = -4i +12, V = 5i - 2j, W=-3i- 6. Find a)...
6-7. Given vectors U = -4i +12, V = 5i - 2j, W=-3i- 6. Find a) 30 - 5V._b) 2V - W'. 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculato
Problem 5. Given a vector space V, a bilinear form on V is a function f : V x V -->R satisfying the following four c...
Problem 5. Given a vector space V, a bilinear form on V is a function f : V x V -->R satisfying the following four conditions: f(u, wf(ū, ) + f(7,i) for every u, õ, wE V. f(u,ū+ i) = f(u, u) + f(ū, w) for every ā, v, w E V. f(ku, kf (ū, v) for every ū, uE V and for every k E R f(u, ku) = kf(u, u) for every u,uE V and for every k...
Exercise 2 : 10 pts (5pts each) 1. Determine if the following vectors are linearly independent...
Exercise 2 : 10 pts (5pts each) 1. Determine if the following vectors are linearly independent vii. Using the definition (i.e. kıvı+k_202 + .. + kūri = 7) viii. Using a determinant a. ū = (-1,2) and = (0,1) b. ü =(3,-6) and 3 = (-4,8) c. ū= (1,2), v = (3,1) and w = (2-2) d. i = (1,4,-3), i = (0,7,1) and w = (0,0,1) e. ü= (-1,2,0), v = (4,1, -3) and w = (10.-2.-6) f. ū=...
problem 1 and problem 2 please , thankyou very much PROBLEM 1 (25%) Find: Let: ū=...
problem 1 and problem 2 please , thankyou very
much
PROBLEM 1 (25%) Find: Let: ū= (1,-1,-2) v = (-2,-2,3) w = (3,-1,1) (a) The angle between ū and w (b) Orthogonal projection of u against v (c) The area of parallelogram formed by u dan v (d) The volume of parallelpiped shaped byū, v, dan w PROBLEM 2 (15%) Determine if these sets of points are coplanar: (a) A(1,1,-3); B(0,1,-2); C(-3, 1, 1); D(2, 1, -4) (b) E(1,1,-1); F(0,1,1);...
7. You are given that u is an angle in quadrant III with sin u -,...
7. You are given that u is an angle in quadrant III with sin u -, and that w is an angle in the first quadrant with tan w = ? . Calculate the exact value of each one of the following: (You should show how you get your answer) (a) cos u (b) tanu (c) sin w (d) cos w (e) sin (u - w) (f) cos (W + u)
2. Let ū= (3,1, -7), ã = (1,0,5). (a) Find the vector component of u along a. (b) Find the vector component of ü orthogonal to ä. (c) Find the angle between u and , in degrees.
8. If ū= 8î - 159 and v = -3i - 4ſ and w = 12 + 69, then find the following: A. 2w - 3ū B. ||2u - 57 C. v. W D. the angle between ü and v E. the direction angle of vector w F. (3 +70).ü G. a vector in the same direction as ū with magnitude of 12 H. a vector orthogonal to vector v with magnitude of 7 I. any vector that is orthogonal...
1. Let {ü, 7,w, i}, where u = (3,-2), v = (0,4), ū = (-1,5) and i = (-6,4). Find the components of the resultants obtained by doing the following linear combinations. a. r = 2ū - 40 b. š= 3ū – +20 +
1. Given the vectors ū=(1,-2,-6) and v = (0,-3,4), a) Find u 6v. b) Find a unit vector in the opposite direction to ū. c) Find (ü.v)v. d) Find 11: e) Find the distance between ū and v. f) Are ū and y parallel, perpendicular, or neither? Explain. g) Verify the Triangle Inequality for ū and ū.
6-7. Given vectors U = -41 +12, V=51-2), W =-31 - 1 6. Find a) 3U - 5V._b) 2V - WI 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculator ok)
6-7. Given vectors U = -4i +12, V = 5i - 2j, W=-3i- 6. Find a) 30 - 5V._b) 2V - W'. 7. a) UW What can you tell from the result? b) angle between U and V (keep one digit after decimal. calculato
Problem 5. Given a vector space V, a bilinear form on V is a function f : V x V -->R satisfying the following four conditions: f(u, wf(ū, ) + f(7,i) for every u, õ, wE V. f(u,ū+ i) = f(u, u) + f(ū, w) for every ā, v, w E V. f(ku, kf (ū, v) for every ū, uE V and for every k E R f(u, ku) = kf(u, u) for every u,uE V and for every k...
Exercise 2 : 10 pts (5pts each) 1. Determine if the following vectors are linearly independent vii. Using the definition (i.e. kıvı+k_202 + .. + kūri = 7) viii. Using a determinant a. ū = (-1,2) and = (0,1) b. ü =(3,-6) and 3 = (-4,8) c. ū= (1,2), v = (3,1) and w = (2-2) d. i = (1,4,-3), i = (0,7,1) and w = (0,0,1) e. ü= (-1,2,0), v = (4,1, -3) and w = (10.-2.-6) f. ū=...
problem 1 and problem 2 please , thankyou very
much
PROBLEM 1 (25%) Find: Let: ū= (1,-1,-2) v = (-2,-2,3) w = (3,-1,1) (a) The angle between ū and w (b) Orthogonal projection of u against v (c) The area of parallelogram formed by u dan v (d) The volume of parallelpiped shaped byū, v, dan w PROBLEM 2 (15%) Determine if these sets of points are coplanar: (a) A(1,1,-3); B(0,1,-2); C(-3, 1, 1); D(2, 1, -4) (b) E(1,1,-1); F(0,1,1);...
7. You are given that u is an angle in quadrant III with sin u -, and that w is an angle in the first quadrant with tan w = ? . Calculate the exact value of each one of the following: (You should show how you get your answer) (a) cos u (b) tanu (c) sin w (d) cos w (e) sin (u - w) (f) cos (W + u)
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