Example 1.4 Area as a VectorWe can use the cross product to describe an area. Usually one thinksof area in terms of magnitude only. However, many applications inphysics require that we also specify the orientation of the area. Forexample, if we wish to calculate the rate at which water in a streamflows through a wire loop of given area, it obviously makes a differencewhether the plane of the loop is perpendicular or parallel to the flow.(If parallel, the flow through the loop is zero.) Here is how the vectorproduct accomplishes this:Consider the area of a quadrilateral formed by two vectors C and D.The area A of the parallelogram is given by

Answered: Image /qna-images/answer/6e622582-845c-4814-ace3-c854b286a8d3.jpg

Answered: Consider the area of a quadrilateral…

Science

Physics

Consider the area of a quadrilateral formed by two vectors C and D. The area A of the parallelogram is given by.

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter2: Vectors

Section: Chapter Questions

Problem 46P: A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with...

See similar textbooks

Related questions

Q: The resultant force is [resultant] and the angle of direction from the positive horizontal axis of…

A: Let the vector MN be vector A and It can be represented as, Here, Ax, Ay, and θA represent the…

Q: show how to resolve the force F into components acting along the u and v axes using the…

A: Resolving force into two components using parallelogram law

Q: : Let x and y be non-parallel vectors. Prove that (x + y) and (x - y) are vectors perpendicular to…

A: For two vectors A→ and B→, the angle between them is θ. The dot product of these vectors…

Q: Dot Product, polar coordinates: If A = 8 < 21 degrees and B = 5 < 62 degrees, find А-В

A: We will first convert the polar coordinates into the cartesian coordinates. Using these coordinates…

Q: Destion If A = - 3.5 i-9.7j and B-- 6.0i+ 8.1 j, what is the angle (less than 180 degrees) between…

Q: Let's try! Using both parallelogram and polygon methods, find the resultant of the following…

Q: The vector orthogonal to 8 +7 and 8 +8 is

Q: Consider the vector whose x- and y-components are given to be -4.9468 and 3.463, respectively.…

A: Given that,x- component of vector Ax=-4.9468y- component of vector Ay=3.463

Q: Show a[1 2 1] direction on a simple cubic unit cell and give the location (in correct notation) for…

A: The required direction vector for [1 2 1] is shown in the figure below.

Q: Given a vector (77, 48, 22) and another vector (4, 49, 67) what is the z-component of their sum?

A: Given that Vector 1 (A)= (77, 48, 22) And , vector 2 (B)= (4, 49, 67) Let i, j and k be the unit…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

Q: Two vectors live with their tail at the same point. When the angle between them is increased by 20…

A: The scalar product between two vectors can be expressed as

Q: Given two vectors A and B. Find the angle between them if A = { 2 , 3, 4} and B = { -2 ,2 -4, }

A: To solve the given question, we will write down the given two vectors in vector form and then we…

Q: The vector product of vectors A and B is maximum, therefore * O O vectors A and B are parallel in…

A: Given: The two vectors are A and B. To find: The condtion for the maximum vector product.

Q: Calculate the angle between vectors A=î+3ĵ+2k and B=î+27+3R

Q: Consider two vectors Å = -5î – 3j + 2k and B = -8j - 2k, find the angle between vectors Å and B.

Q: Consider the vectors A = (-8.1,5.4) and B = (10.7,-9.1), such that A - B +2.7C = 0. %3D

Q: The cartesian coordinate form of two vectors are: (-2, 0, 2) and (1, 1, 1). Find the angle between…

A: Given: The cartesian coordinate of the vectors is (x1, y1, z1)=(-2, 0, 2) and (x2, y2, z2)=(1, 1,…

Q: A force vector has magnitude F makes an angle of 69° with respect to the x-axis of a Cartesian space…

A: Given, a force vector has magnitude F makes an angle of x=69° with respect to the x-axis of a…

Q: 6 units and is in the direction of +x-axis. Vector B has a magnitude 4 units and lies in the…

A: Given:- Vector B lies in x-y plane at an angle 30°with x-axis To find:- Formula used:-

Q: What is the angle e between vectors Ã and B if A = 3 i +4 ĵ and B = 8 î – 6 j?

Q: what angle 0 is the plane inclined?

Q: * = • Two vectors A and B have magnitudes A 3.00 and B =3.00, Their vector product is A × B=5.00k +…

Q: if A⃗ =2i+3j+6kA→=2i+3j+6k and A⃗ =3i−4j+2kA→=3i−4j+2k, then the angle between the two vectors is

Q: In unit vector notation, å, and åz vectors are given as å, = -3î + 6ĵ + 2k and åz = -2î – 5j + 2k.…

A: Introduction : Angle between two vectors can be found by taking their dot products. Given :…

Q: Let vector A point from the origin into the second quadrant of the xy plane and vector B point from…

A: When subtracting vectors, the rule is to graph the first two from the origin and then connect them…

Q: Two vectors Á and B have precisely equal mag- nitudes. For the magnitude of A + B to be 100 times…

Q: vector algebra dot product of (i+j+k) and (i-j+k) is?

A: Given : Vector 1 →V1→=i^+j^+k^ Vector 2 →V2→=i^-j^+k^

Q: Find the measures of the angles between the diagonals of the rectangle whose vertices are A = (5,…

A: Vertices of rectangle: A(5,6), B(8,12), C(-40,36), D(-43,30) When we'll plot these vertices on…

Q: Derive the matrix for rotation around the x-axis 30

A: Basics of Rotation matrix: Rotation matrix is used to perform a rotation in Euclidean space. The…

Q: Use the law of sines and the law of cosines, in conjunction with sketches of the force polygons, to…

A: Given: The resultant magnitude R and the angle θ between the x-axis and the line of action of the…

Q: : Express the vector 2i + 3j – k in the primed triad i'j'k' in which the x'y' axes are ated about…

Q: Consider the two vectors given in the figure, what is their SUM in the unit vector notation?

Q: The resultant of two vectors which have equal magnitudes is another vector of magnitude equal to…

A: The magnitude of the two vectors is the same and the magnitude of the resultant vector is also the…

Q: Given the vectors i =(- 3, 7, 4] and y = [- 6, 0, 8], determine b) proj š. a) The angle between i…

Q: 7.60 In Problem 7.59, what is the vector component of F parallel T to the surface?

A: As A is at the centre of the plane so, The coordinate of A will be half of the plane's coordinate:-…

Q: .Calculate the area of the parallelogram whose two adjacent sides are formed by the vectors. A = 3i…

Q: Given two vectors A=3i - 4k and B = -5j. What is the angle between these vectors?

Q: Let be two vectors, such that a=(3+2j-2k) cm and b=(2î+2j+k) cm, calculate: 1) The angle between the…

Q: A vector makes a 22˚ angle with the horizontal and has a magnitude of 6. Decompose the vector and…

A: Given data: θ=22°V=6 Need to determine the given vector in the form of vector.

Q: 2)1F the Volume is egual to Zero ,then the all Vectors line in the same planc. a.T b.F

A: Given volume of parallelepiped formed by the vectors is zero

Q: Given a vector (54, 46, 48) and another vector (18, 37, 7) what is the z-component of their sum?

A: Given - Cordinateof vector A = (54, 46, 48) Cordinateof vector B= (18, 37, 7)Now vector -A→ = (…

Q: What is the angle between vectors A- 2i + 3j + k and B- 3i • 2j • K?

A: Given Data: The vector A is: A=2i+3j+k The vector B is: B=3i+2j+k

Q: Calculate the area formed by the two vectors A =3 i +2j+k and B = i-3 j-2k. Also find out the angles…

Q: What direction does the vector L point in for a plane rotating?

A: To determine: The direction of the vector angular momentum 'L' that is pointing in a rotating plane

Q: What is the angle of the 10X force?

Question

100%

Example 1.4 Area as a Vector
We can use the cross product to describe an area. Usually one thinks
of area in terms of magnitude only. However, many applications in
physics require that we also specify the orientation of the area. For
example, if we wish to calculate the rate at which water in a stream
flows through a wire loop of given area, it obviously makes a difference
whether the plane of the loop is perpendicular or parallel to the flow.
(If parallel, the flow through the loop is zero.) Here is how the vector
product accomplishes this:
Consider the area of a quadrilateral formed by two vectors C and D.
The area A of the parallelogram is given by

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

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

Similar questions

Answer the following questions using the prescribed format and provide complete and neat solution to each of theproblems. May I clarify 2b. There is a correction on the hint provided what we are trying to do is project BC to vector BA (component of BC on BA), hence it should be uBA dot BC NOT uBA dot AC. vector AC should not be used 2) On figure 3 and 4, a vector quantity (AC), presumably a force, is placed on point B and is pointing towards pointC. The coordinates of point C is (5.5, 2, 6.3)a) What is the vector representation of BC?b) What is the magnitude of the component of BC along BA?Hint get the unit vector of BA, then get the dot product of (unit vector of BA) and the (vector BC).
The volume of a sphere is given byV=(4/3)πr^3, whereris the sphere’s radius. For solid spheres with the same density – made, for example, from the samematerial – mass is proportional to volume. The table below lists measures of deameterand mass for different steel balls. (a) Determine the quantity that, when you plot mass against it, should yield a straightline. (b) Make your plot, establish a best-fit line, and determine its slope (which in thiscase is proportional to the spheres’ density Diameter (cm) 0.75 1.0 1.56 2.16 2.54 Mass(g) 1.81 3.95 15.8 38.6 68.2
A fly enters through an open window and zooms around the room. In a Cartesian coordinate system with three axes along three edges of the room, the fly changes its position from point b(4.0m,1.5m,2.5m) to point e(1.0m,4.5in,0.5m) . Find the scalar components of the fly’s displacement vector and express its displacement vector in vector component form. What is its magnitude?
Derive a formula for the centroid of section U in the figure below, in terms of r and h and in relation to the x and y axes
Please try not to use derivatives or integrals to calculate stuff. Thank you.
Solve the following problems and provide your complete solution including the given, formula, and solving.
Write the solution legibly.
Pls do fast and i will give like for sure Solution must be in typed form
Imagine a very huge industrial metallic bucket is in the shape of the frustum of a right circular cone whose top and bottom diameters are 10 m and 4 m respectively and a height of 4 m. a) what is the curved surface area of the bucket? b) what is the volume of water if it’s to be filled to the brim if the thickness of the metal is 0.60 meters including the base?
Here are the equations I only need help with part e please
A trapper walks a 5.0-km straigt4ine distance from his cabin to the lake, as shown in the following figure. Use a graphical method (the parallelogram rule) to determine the trapper’s displacement directly to the east and displacement directly to the north that sum up to his resultant displacement vector. If the trapper walked only in directions east and north, zigzagging his way to the lake, how many kilometers would he have to walk to get to the lake?
From fundamental electronics, the current flowing through a capacitor at any instant of time is equal to the capacitance times the rate of change of voltage (electromotive force) across the capacitor, I = C( dE/dt) Write the primary dimensions of both sides of this equation, and verify that the equation is dimensionally homogeneous. Show all your work.