Homework Answers
static cross(v1, v2) {
return new Vector(v1.y*v2.z - v1.z*v2.y, v1.z*v2.x - v1.x*v2.z, v1.x*v2.y - v1.y*v2.x)
}
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// returns the cross product of the two input vectors "v1" and...
Problem 4 A set of vectors is given by S = {V1, V2, V3} in R3...
Problem 4 A set of vectors is given by S = {V1, V2, V3} in R3 where eV1 = 1 5 -4 7 eV2 = 3 . eV3 = 11 -6 10 a) [3 pts) Show that S is a basis for R3. b) (4 pts] Using the above coordinate vectors, find the base transition matrix eTs from the basis S to the standard basis e. Then compute the base transition matrix sTe from the standard basis e to the...
Describe what each code snippet does and how it might be used in Statics. Describe in...
Describe what each code snippet does and how it might be used in Statics. Describe in general terms what Statics calculation is being performed by each code snippet. What is input to the calculation and what results are given? Give definitions not numbers. Hint: all arrays are components of vectors [ x, y, z ]. Code 1 V1 = [ 0, 1, 2 ]; V2 = [ 3, -4, 5 ]; x = 1; y = 2; z = 3;...
Using java fix the code I implemented so that it passes the JUnit Tests. MATRIX3 public...
Using java fix the code I implemented so that it passes the JUnit Tests. MATRIX3 public class Matrix3 { private double[][] matrix; /** * Creates a 3x3 matrix from an 2D array * @param v array containing 3 components of the desired vector */ public Matrix3(double[][] array) { this.matrix = array; } /** * Clones an existing matrix * @param old an existing Matrix3 object */ public Matrix3(Matrix3 old) { matrix = new double[old.matrix.length][]; for(int i = 0; i <...
Problem 3 - Find the dot product between vectors A and B where Pa Worksheet 6 Vector Dot and Cross Products Problem 4...
Problem 3 - Find the dot product between vectors A and B where Pa Worksheet 6 Vector Dot and Cross Products Problem 4 - Use the vector dot product to find the angle between vectors A and B where: Defining the Vector Cross Product: It turns out that there are some weird effects in physics that require us to invent a new kind of vector multiplication. For example, when a proton moves through a magnetic field, the force on the...
6. 2D vectors Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a)...
6.
2D vectors
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (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? &Define a unit vector. Give an example of a...
Defining the cross product The cross product of two nonzero vectors
Defining the cross product The cross product of two nonzero vectors \(\vec{u}\) and \(\vec{v}\) is another vector \(\vec{u} \times \vec{v}\) with magnitude$$ |\vec{u} \times \vec{v}|=|\vec{u}||\vec{v}| \sin (\theta), $$where \(0 \leq \theta \leq \pi\) is the angle between the two vectors. The direction of \(\vec{u} \times \vec{v}\) is given by the right hand rule: when you put the vectors tail to tail and let the fingers of your right hand curl from \(\vec{u}\) to \(\vec{v}\) the direction of \(\vec{u} \times \vec{v}\)...
6 ture Supplement 4: Intro Vectors Worksheet B a vector (graphical, verbal, or mathematical) that is...
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...
Problem 3 - Find the dot product between vectors A and B where Pa Worksheet 6...
Problem 3 - Find the dot product between vectors A and B where Pa Worksheet 6 Vector Dot and Cross Products Problem 4 - Use the vector dot product to find the angle between vectors A and B where: Defining the Vector Cross Product: It turns out that there are some weird effects in physics that require us to invent a new kind of vector multiplication. For example, when a proton moves through a magnetic field, the force on the...
7. Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b)...
7.
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (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? &Define a unit vector. Give an example of a unit vector...
Using C++ to write .cpp and .h file. Main function and sample output are given. The...
Using C++ to write .cpp and .h file. Main function and sample
output are given. The task is to write a vector class for dynamic
allocation.declare the the class named vector with the required
attributes. The task are defined in the main function.
#include <iostream> #include "vector.h". #define LOG(x,y) std::cout << x << y « std::endl; #define INFO(x) std::cout << "[INFO]: #define WARNING(x) std::cout <« "[WARNING]: "<< x <« std: :endl; << x << std::endl; " « x < std::endl;...
Problem 4 A set of vectors is given by S = {V1, V2, V3} in R3 where eV1 = 1 5 -4 7 eV2 = 3 . eV3 = 11 -6 10 a) [3 pts) Show that S is a basis for R3. b) (4 pts] Using the above coordinate vectors, find the base transition matrix eTs from the basis S to the standard basis e. Then compute the base transition matrix sTe from the standard basis e to the...
Problem 3 - Find the dot product between vectors A and B where Pa Worksheet 6 Vector Dot and Cross Products Problem 4 - Use the vector dot product to find the angle between vectors A and B where: Defining the Vector Cross Product: It turns out that there are some weird effects in physics that require us to invent a new kind of vector multiplication. For example, when a proton moves through a magnetic field, the force on the...
6.
2D vectors
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (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? &Define a unit vector. Give an example of a...
Defining the cross product The cross product of two nonzero vectors \(\vec{u}\) and \(\vec{v}\) is another vector \(\vec{u} \times \vec{v}\) with magnitude$$ |\vec{u} \times \vec{v}|=|\vec{u}||\vec{v}| \sin (\theta), $$where \(0 \leq \theta \leq \pi\) is the angle between the two vectors. The direction of \(\vec{u} \times \vec{v}\) is given by the right hand rule: when you put the vectors tail to tail and let the fingers of your right hand curl from \(\vec{u}\) to \(\vec{v}\) the direction of \(\vec{u} \times \vec{v}\)...
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...
Problem 3 - Find the dot product between vectors A and B where Pa Worksheet 6 Vector Dot and Cross Products Problem 4 - Use the vector dot product to find the angle between vectors A and B where: Defining the Vector Cross Product: It turns out that there are some weird effects in physics that require us to invent a new kind of vector multiplication. For example, when a proton moves through a magnetic field, the force on the...
7.
Lec ture Supplement 4: Intro Vectors Worksheet B Provide an example of a) ID b) 2D c) 3D a vector (graphical, verbal, or mathematical) that is in: (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? &Define a unit vector. Give an example of a unit vector...
Using C++ to write .cpp and .h file. Main function and sample
output are given. The task is to write a vector class for dynamic
allocation.declare the the class named vector with the required
attributes. The task are defined in the main function.
#include <iostream> #include "vector.h". #define LOG(x,y) std::cout << x << y « std::endl; #define INFO(x) std::cout << "[INFO]: #define WARNING(x) std::cout <« "[WARNING]: "<< x <« std: :endl; << x << std::endl; " « x < std::endl;...
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