Consider the vector v = (2,3,1). What must be the coordinates of the three-dimensional unit vector u so that the dot product u·v is as large as possible?
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Consider the vector v = (2,3,1). What must be the coordinates of the three-dimensional unit vector u so that the dot product u·v is as large as possible?
the furthest i could get is that the dot product between vector N and vector V, as well as vector X and vector V must be zero but that's about it. I get stuck when trying to use the cosine relation with the dot product but since the question doesn't allow me to write it in terms of an angle, i can't really use that. If someone could show me how this would help incredibly! 3. X is an unknown...
2. Consider a three-dimensional Universe. A vector of this space, starts from the origin of the coordinate system and has the tip described by the coordinates 1, 0, a) Write the matrix that describes a rotation of this three dimensional vector about the Oz axis by an angle of 45° Both the initial and the final coordinates have the same origin. b) Calculate the projections (of the tip) of this vector along the new axes of coordinates.
Problem 1 - Find all six possible dot products between the unit vectors of Cartesian coordinates. Find: and k and then values of θ for each of the dot products Do this by finding the magnitudes of you are solving for. Page 1/8 Worksheet 6- Vector Dot and Cross Products Problem 2- Use the answers to problem 1 to find a general equation for multiplying two vectors assuming you already know their components. To do this, substitute the unit vector...
Exercise 1. Consider the complex vector space Cendowed with the complex dot product, and the 11 01 following vectors: vi = i,v = 1, uz = 0,01 = 1 . Is vi orthogonal to any of the other three vectors? What about uz and ?
Properties of the dot product Please help! theoretical calculus 2. Some properties of the dot product: (a) The Cauchy-Schwartz inequality: Given vectors u and v, show that lu-vl lullv1. When is this inequality an equality? (Hint: Use the relationship between u-v and the angle θ between u and v.) (b) The dot product is positive definite: Show that u u 2 0 for any vector u and that u u 0 only when u-0. (c) Find examples of vectors u,...
- 1 15. Let u= and v= 0 1. What is the dot product of u and v? -1] d) e) 2 L 1] b)-2 a) -1 c)0
Let V, W, and U be three finite dimensional vector spaces over R and T:V + Wand S : W → U be two linear transformations. Show that null(SoT) < null(T) + null(S)
Q7 8 Points Let V, W, and U be three finite dimensional vector spaces over R and T:V + Wand S : W → U be two linear transformations. Q7.1 4 Points Show that null(So T) < null(T) + null(S) Please select file(s) Select file(s) Save Answer Q7.2 4 Points Show that rank(S • T) > rank(T) + rank(S) – dim(W) (Hint: Use part (1) at some point)
6. Assume that ( U U ), ( V V ) and (W, w) are three normed vector spaces over R. Show that if A: U V and B: V W are bounded, linear operators, then C = BoA is a bounded, linear operator. Show that C| < |A|B| and find an example where we have strict inequality (it is possible to find simple, finite dimensional examples).
Let V, W, and U be three finite dimensional vector spaces over R and T:V + Wand S : W → U be two linear transformations. Show that rank( ST) > rank(T) + rank(S) - dim(W)