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Consider the points u(1, 1,-1), v (a, 2,-1) and w (1,2,-1) in R3, where a e R. There are two possible values of a for which u, v and w will form an isosceles triangle. a) Find one of these values. (b) Determine the angle between the equal sides of the triangle.
Consider the points u(1, 1,-1), v (a, 2,-1) and w (1,2,-1) in R3, where a e R. There are two possible values of a for which u, v...
Exercise Set Chapter 3 Q1) Let u = (2, -2, 3), v = (1, -3, 4), and w=(3,6,-4). a) Evaluate the given expression u + v V - 3u ||u – v| u. V lju – v|w V X W ux (v x W) b) Find the angle 8 between the vector u = (2,-2,3) and v = (1, -3,4). c) Calculate the area of the parallelogram determined by the vector u and v d) Calculate the scalar triple product...
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lit khd where it came from 4. You do not need to simplify results, unless otherwise stated. 1. (20pts.) Indicate whether each of the following questions is True or False by writing the words "True" or "False" No explanation is needed. (a) If S is a set of linearly independent vectors in R" then the set S is an orthogonal set (b) If the vector x is orthogonal to every vector in a subspace W...
3. Consider the following vectors, where k is some real number. H-11 Lol 1-1 a. For what values of k are the vectors linearly independent? b. For what values of k are the vectors linearly dependent? c. What is the angle (in degrees) between u and v? 4. Here are two vectors in R". Let V = the span of {"v1r2} a. Find an orthogonal basis for V (the orthogonal complement of V). b. Find a vector that is neither...
1. (10 points) Consider the vectors u = 0 and v = | 2 [E (a) Find cosine of the angle between two vectors. Is the angle acute, obtuse, or neither? (b) Find p = projspan{v}u and verify that u-p is orthogonal to v.
8. If ü= 8i - 15j and = -31 - 4; and w = 121 + 6j, then find the following: A. 2w - 3ü B. ||2u - 501 C. J. D. the angle between ü and v E. the direction angle of vector w F. (3x + 70). a vector in the same direction as u with magnitude of 12 a vector orthogonal to vector V with magnitude of 7 any vector that is orthogonal to the vector w...
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16) (6pts) Find the projection of ü onto w. a) Find ui --Son 347 2 25 26 b) Find 펄 orthogonal to in such that iiitül ü 2 Page Score Check ( 13 For problems on this page, use the vectors described graphically here. Your work should include correct vector notation of u, i,and w 13) What is (w+u) v E xplat 3 U=(2、1) w (3, .. 4) 14) Find the cxact magnitudes of i,...
4. Consider the vector space V = R3 and the matrix 2 -1 -1 2 -1 -1 0 2 We can define an inner product on V by (v, w) = v'Mw. where vt indicates the transpose. Please note this is NOT the standard dot product. It is a inner product different (a) (5 points) Apply the Gram-Schmidt process to the basis E = {e1,e2, e3} (the standard basis) to find an orthogonal basis B.
4. Consider the vector space...
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...
Let u = [1, 3, -2], v = [-1, 1, 1], w = [5, 1, 4]. a) Check if the system of vectors {u,v,w} is an orthogonal or othonormal basis of E3. b) Find the coordinates of the vector [1,0,1] in this basis.