### Understanding Vector Cross Product Components#### Problem ContextVector **u** has a **POSITIVE** x-component, **POSITIVE** y-component, and **ZERO** z-component. Vector **v** has a **NEGATIVE** x-component, **POSITIVE** y-component, and **POSITIVE** z-component.#### QuestionWhat is true about the cross product **u × v**?#### Answer Options- There is not enough information to know anything.- It has **NEGATIVE** x-component, **NEGATIVE** y-component, **NEGATIVE** z-component- It has **POSITIVE** x-component, **NEGATIVE** y-component, **NEGATIVE** z-component- It has **POSITIVE** x-component, **NEGATIVE** y-component, **POSITIVE** z-component#### Solution ExplanationTo determine the components of the cross product **u × v**, we can use the formula for the cross product of two vectors in three-dimensional space:Given\[ \mathbf{u} = (u_x, u_y, u_z) \]\[ \mathbf{v} = (v_x, v_y, v_z) \]The cross product **u × v** is given by:\[ \mathbf{u} \times \mathbf{v} = \left( u_y v_z - u_z v_y, u_z v_x - u_x v_z, u_x v_y - u_y v_x \right) \]Substitute the given values:\[ \mathbf{u} = (u_x > 0, u_y > 0, u_z = 0) \]\[ \mathbf{v} = (v_x < 0, v_y > 0, v_z > 0) \]So,\[ u \times v = \left( (u_y \cdot v_z - 0 \cdot v_y), (0 \cdot v_x - u_x \cdot v_z), (u_x \cdot v_y - u_y \cdot v_x) \right) \]\[ = (u_y \cdot v_z, -u_x \cdot v_z, u_x \cdot v_y - u_y \cdot v_x) \]### Interpreting the Signs:1. **u_y \cdot v_z**: - u_y > 0 (

Answered: Image /qna-images/answer/c9565e65-e75f-4828-a7d8-df0fcc0615b7.jpg

Vector u has POSITIVE x-component, POSITIVE y-component and ZERO z-component. Vector v has NEGATIVE x-component, POSITIVE y-component and POSITIVE z-component. What is true about u x v? There is not enough information to know anything. O It has NEGATIVE x-component, NEGATIVE y-component, NEGATIVE z-component O It has POSITIVE×-component, NEGATIVE y-component, NEGATIVE z-component It has POSITIVE x-component, NEGATIVE y-component, POSITIVE z-component

Vector u has POSITIVE x-component, POSITIVE y-component and ZERO z-component. Vector v has NEGATIVE x-component, POSITIVE y-component and POSITIVE z-component. What is true about u x v? There is not enough information to know anything. O It has NEGATIVE x-component, NEGATIVE y-component, NEGATIVE z-component O It has POSITIVE×-component, NEGATIVE y-component, NEGATIVE z-component It has POSITIVE x-component, NEGATIVE y-component, POSITIVE z-component

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: Let v1 vector=[−4 h] and v2 vector =[−10 20] (check image for reference) Then span(v1…

Q: Find the unit vector in the direction of <4,2>

Q: 4. Express PQ-RQ+SR-PS+RS as a single vector.

A: Expression

Q: nd the length of the vector fo raight line joining the points 5,2). Also find the angle made

A: Given, The vector is formed by the straight line joining the points 1,3 and5,2. The length is to be…

Q: express vector as a product of its length and direction. 1/(3)^1/2 i + 1/(3)^1/2 j + 1/(3)^1/2 k

A: Let the given vector is: v=13i+13j+13k

Q: 2. Find the angle between vector [2, -5,7] and vector [6,4,1]

A: Vector [2,-5,7] and vector [6,4,1] We have to find angle between these two vectors

Q: ctor is a quantity characterized by only a positive or negative number that represents its magnitude…

Q: what are the examples of contravarient and covariant tensors?

A: Example of Covariant tensor: A'i=aijAj

Q: Hiwil show that_Viz 3i+6j_and_V=-i-zj have offosite direction.

A: We have to prove that vectors have opposite direction.

Q: Define direction vector.

A: Define direction vector.

Q: A = [-2,4,-2,-4, 2,-6,-3,1, -3,8,2,-3, 0,2,5,3] Find a non-zero vector R^4…

Q: A = [-2,4,-2,-4, 2,-6,-3,1, -3,8,2,-3, 0,2,5,3] Find a non-zero vector…

A: Given matrix is A=-24-2-42-6-31-382-30253

Q: Describe the relationship between the point (10,13) and the vector

A: We have to describe the relationship between the point (10, 13) and vector <10, 13>

Q: How do you know if 3 vectors span R^3? Is there any example?

Q: (b) Find the points in which the required line in part (a) intersects the coordinate planes.

Q: Which of the following vectors is opposite of the given vector below?

Q: Suppose the equation ax + by = c corresponds to the vector (a, b, c). To what equation will…

A: Given that:The equation ax+by=c corresponds to the vector ⟨a,b,c⟩. (1).The given vector is:…

Q: Find vector z + vector y if vector z= and vector y= . graph

Q: Determine the figene valves and Vector for 2 A=-1 2 -2

A: (A-λI)X=0 A= given matrix λ=constant I=identity matrix

Q: The contrasts (-3, 1 1 1) and (0, 0 , -1, 1) are orthogonal? Is it True or False?

A: Orthogonal contrasts: A set of contrasts in which, for any distinct pair, the sum of the…

Q: Line E goes through the points (1, 5, 2) and has the direction vector ⟨2, 2, 3⟩. Line F goes through…

Q: Write out the expressions a- Va in index notation for vector a

A: Let us consider a vectora→ = a1i^ +a2j^ +a3k^where a1 , a2, a3 are functions of (x1, x2 & x3)and…

Q: Given u = ( 5, -3, 8) and v (k, 2, 4) calculate k, by using only vector | = 2 7| concepts, where…

A: Topic = Vector

Q: :) What is a 2b2+|a.b|²? Let a = 0 and b = -2 0 2 be two vectors.

Q: Find the vector determined by 18 || = B = {[.]. 9 6 12 3 9 2 -8 " where B = 3 [-]

Concept explainers

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.

Question

### Understanding Vector Cross Product Components

#### Problem Context
Vector **u** has a **POSITIVE** x-component, **POSITIVE** y-component, and **ZERO** z-component.
Vector **v** has a **NEGATIVE** x-component, **POSITIVE** y-component, and **POSITIVE** z-component.

#### Question
What is true about the cross product **u × v**?

#### Answer Options
- There is not enough information to know anything.
- It has **NEGATIVE** x-component, **NEGATIVE** y-component, **NEGATIVE** z-component
- It has **POSITIVE** x-component, **NEGATIVE** y-component, **NEGATIVE** z-component
- It has **POSITIVE** x-component, **NEGATIVE** y-component, **POSITIVE** z-component

#### Solution Explanation
To determine the components of the cross product **u × v**, we can use the formula for the cross product of two vectors in three-dimensional space:

Given
\[ \mathbf{u} = (u_x, u_y, u_z) \]
\[ \mathbf{v} = (v_x, v_y, v_z) \]

The cross product **u × v** is given by:
\[ \mathbf{u} \times \mathbf{v} = \left( u_y v_z - u_z v_y, u_z v_x - u_x v_z, u_x v_y - u_y v_x \right) \]

Substitute the given values:
\[ \mathbf{u} = (u_x > 0, u_y > 0, u_z = 0) \]
\[ \mathbf{v} = (v_x < 0, v_y > 0, v_z > 0) \]

So,
\[ u \times v = \left( (u_y \cdot v_z - 0 \cdot v_y), (0 \cdot v_x - u_x \cdot v_z), (u_x \cdot v_y - u_y \cdot v_x) \right) \]
\[ = (u_y \cdot v_z, -u_x \cdot v_z, u_x \cdot v_y - u_y \cdot v_x) \]

### Interpreting the Signs:
1. **u_y \cdot v_z**:
- u_y > 0 (

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Vector Space$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

(у-3) -dy -бу+1 у2
Pls help ASAP
Find Vector A and B such that A is parallel to <2,1,-1>, B is perpendicular to <2,1,-1> and A + B = <-1,5,7> if you already answered this one, please dont answer it anymore
If vector r = {4, 9) and s= (7,-5) then which is r-s? b C r-s=(-3, 14) r-s=(3, -14) r-s=(-11,4) r-s=(11,4)
Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector 1 Which of the following points (given by their coordinates) lie on | 1? Select one: a. (-3, 1, -1) b. (-2, -1, 0) c. (-3, 2,-1) d. (-4, 3, 0)
What is meant by orthogonal?