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 poss...
Problem l: Let u, v and w be three vectors in R3 (a) Prove that wlv +lvlw bisects the angle between v and w. (b) Consider the projection proj, w of w onto v, and then project this projection on u to get proju (proj, w). Is this necessarily equal to the projection proj, w of w on u? Prove or give a counterexample. (c) Find the volume of the parallelepiped with edges formed by u-(2,5,c), v (1,1,1) and w...
I can't follow the answer please explain. 7. (a) Consider the rectangle S in R3 with vertices (0,0,0), (1, 1,o), (a.1,2), and (0,0,2). Give a parameterization of S of the form r(u, v) where 0susland 0s v s1. (2 points) 2 1,2) 刁ㄚ r(u, u) = , u 7. (a) Consider the rectangle S in R3 with vertices (0,0,0), (1, 1,o), (a.1,2), and (0,0,2). Give a parameterization of S of the form r(u, v) where 0susland 0s v s1. (2...
(3) Consider f: R3- R3 defined by (u,, w)-f(r, y, :) where u=x w = 3~. Let A = {1 < x < 2, 0 < xy < 2, 0 < z < 1). Write down (i) the derivative Df as a matrix (ii) the Jacobian determinant, (ii) sketch A in (x, y. :)-space, and iv) sketch f(A) in (u. v, w)-space.
1) Consider u = 2 -2), v 1 2 and w=3, where a is real number. -- a) Find the length of w. b) Find the distance between u and v. c) Find a unit vector in the direction of w. d) Find the real number a such that v and w are orthogonal. e) Find the angle 0 between u and v. remote proctor each individualsheet of paper front and
1 3. Consider the vector v= (-1) in R3. Let U = {w € R3 :w.v=0}, where w.v is the dot product. 2 (a) Prove that U is a subspace of R3. (b) Find a basis for U and compute its dimension. 4. Decide whether or not the following subsets of vector spaces are linearly independent. If they are, prove it. If they aren't, write one as a linear combination of the others. (a) The subset {0 0 0 of...
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.
0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V) 0 17 (2 points) Find the projection of5onto the subspace W of R3 spanned by6 U- -1 projw (V)
O-a22 points STig2 3.3055 Find the area of a triangle with sides of length 13 and 29 and included angle 20, (Round your answer to one decimal place.) Need Help? vaach Bad it te to a Tutor O-022 points STig2 3.3008 29 An isosceles triangle has an area of 33 cm, and the angle between the two equal sides is Sm/6. What is the length of the two equal sides? (Round your answer to one decimal place.) cm Need Help?...
. Consider the function v(r) r(r 1/2) (r-1) for r e (0, 1]. Determine the transformed function u(E) introduced in the previous question. Show that u(E)dE = 0. (Hint: you can do this without evaluating the function.) Determine the values of the midpoint rule,the simple trapezoidal rule (with two point s) and of the Gaussian rule with 2 quadrature points. What do you observe about the accuracy of these rules? 10pts . Consider the function v(r) r(r 1/2) (r-1) for...
17 Find the orthogonal complement of the following. a. U = sp({(3,-1,2)}) in R3. b. V=({(1,3,0), (0,2,1))) in R3. Do this both algebraically and geometrically. Compare with part a. c. W=sp({1+x}) in 81 (-1,1]).