Part III: Numerical Analysis Comprehension 1. Show a mathematical formula to calculate the dot product of...
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,...
PART TWO. Open Response. SHOW YOUR WORK. Draw boxes an One vector is given by -8i + 5 -2ik. Another vector i ban s heype around your answers. and is directed 37° counterclockwise from the positive x-axais (a) (1 point) Find the dot product T., using the componen (b) (1 point) Use the definition of the dot product to has a magnitude of 22 units find the angle φ between u and ซี. ขึ u x w (c) (1 point)...
6
ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is in: Provide an example of a) ID b) 2D c) 3D (graphi Outline the main vector operations we will use in class: a) Vector Addition b) Vector Subtraction c) Scalar Multiplication d) Vector Dot Product e) Vector Cross Product What is a resultant vector? 4 What is the component of a vector? 3,Define a unit vector. Give an example of a unit vector in...
pls answer 4,5,6 and 7
An) a) Find the magnitude of both vectors. b) Find dot product and cross product of both vectors c) Find the projection of w onto v 2) Let а:31 + 5, + 7k and b--6r +-10, + mk where m e R. a) Find the value for m such that vectors are orthogonal b) Find the value of m such that the cross product of the vectors is zero 3) a) Find the distance from...
1) The force and displacement vectors are given below in component form, calculate the Dot product fog of the force and displacement vector and determine the angle (6) between the vectors? = (+12N)&+ (-18 N)9+ (+5 N)2 * = (+2 m)X + (+4 m)+(-3 m) 28 Nm and 0 = 0° + 111 Nm and o = 21° - 63 Nm and p = 58° - 33 Nm and O = 146° - 28 Nm and 0 = 120° -...
[3] Given: u = -81 + 6j v = 1-3 w = 41 - 8j T= -101 Point Pat (-7, -2), point at (-9, 11), and point Rat (8.-15) Five of the following six parts are each worth 3 points. Part b is worth 5 points. a) Find the position vector, in x + yj form, for the vector whose initial point is R and whose terminal point is g. b) Sketch the position vector determined by point P, and...
[3] Given: u = -8i + 6 v = i- j w = 4i - 8j T = -10i Point Pat (-17, -v2), point at (-9, 11), and point Rat (8, -15) Five of the following six parts are each worth 3 points. Part b is worth 5 points. a) Find the position vector, in xi + yj form, for the vector whose initial point is R and whose terminal point is 9. b) Sketch the position vector determined by...
[3] Given: u = -81 +6j vi- j = -101 Point Pat (-17, -v2), point 9 at (-9, 11), and point Rat (8.-15) Five of the following six parts are each worth 3 points. Part b is worth 5 points. a) Find the position vector, in x + yj form, for the vector whose initial point is R and whose terminal point is g. b) Sketch the position vector determined by point P, and then find its magnitude and direction....
Please answer all questions for UPVOTE
LOCATION: Cleveland, Ohio
DREAM LOCATION: Rome, Italy
PRECALCULUS: VECTORS Directions: Suppose that you plan to take a trip to your dream destination. You would like to know the shortest distance between your starting point and your destination. When calculating distances on a plane, you need only consider two dimensions because you are on a flat surface. However, when finding distances between two points on Earth, you must take into the account the curvature of...
5.4.17. Construct an example using the standard inner product in R to show that two vectors x and y can have an angle between them that is close to /2 without хту being close to 0, Hint: Consider n to be large. and use the vector e of all 1's for one of the vectors.