Answered: Show that the linear combinations h1 =…

Science

Physics

Show that the linear combinations h1 = s + px + py + pz and h2 =s − px − py + pz are mutually orthogonal.

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter1: Matrices, Vectors, And Vector Calculus

Section: Chapter Questions

Problem 1.41P: For what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?

See similar textbooks

Related questions

Q: 2.) A = 8i + 4j – 2k lb B = 2j + 6k ft C = 3i – 2j + 4k ft a.) Å · B b.) Ảx C c.) Find the angle…

A: GivenA = 8i + 4j — 2k lbB = 2j + 6k ftC = 3i — 2j + 4k ft

Q: 4.2 m 5m A 5m long ladder is leaning against a wall of height 4.2m, as shown. The angle (e) made by…

Q: Which of the following functions of the complex variable z = r+iy = ret0 are analytic and which ones…

A: Note :- We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Suppose i = 31 + 8j – 18k and ū 31 + 3j + k. Compute the following: %3D The cosine of the angle…

Q: >> B-Day: Length 6/8 1/8/2022 e 5:09:22 Direc X-va lue Y-value ==== 7.9 334.4 7.10 -3.40 18.5 150.1…

A: Here, the problem is to add the vectors A,B,C,D and E. Given, Length of vector A = 7.9 units. Angle…

Q: Find the x- and y-components of R = 2A − B if A has components Ax = 18.6 m and Ay = 13.0 m…

A: Given Data: The equation for the component R is, R=2A-B The x component of A is, Ax=18.6 m The y…

Q: Consider the curve described by the parametric equations E = 2 cos t, y = 3 sin t For which value of…

Q: Let f(x)= 4xex - sin(5x). Find the third derivative of this function. Note ex is denoted as e^x…

Q: MA = 61.0 N at 17.0° north of east F, = 38.0 N at 64.0° north of east F = 54.0 N at 82.0° %D North…

A: Component of vector along x axis = ACosθ Component of vector along y axis = Asinθ

Q: Please help ASAP

A: To find : the value on the y axis represented by point P

Q: For the following three vectors, what is 3 C (3A x B A = 3.00î + 4.00 – 3.00k B=-4.00î + 3.0oj +…

A: A→ = 3i^ + 4j^ - 3k^B→ = -4i^ + 3j^ + 2k^C→ = 6i^ - 7j^3.C→ = 3.(6i^ - 7j^)= 18i^ - 21j^

Q: From the followng equations x=1.125t + 0.0931 y= -4.9807t2 + 2.3917t + 0.2347: What is the intial…

A: Given data *The first given equation is x = 1.125t + 0.0931 *The second given equation is y =…

Q: Given the function D= 3x²y - y³z², find the gradient VQ. b. a. 6xyî+ (3x² - 3y²z²)ĵ- 2y³zk…

A: Given, Φ = 3x2y - y3z2

Q: Find the angle between vectors D = (2.0 i - 4.0 j + k) m , and B= ( -2.0 i +3.0j + 2.0 k ) m A.…

A: Given- D = (2.0 i - 4.0 j + k) m B= ( -2.0 i +3.0 j + 2.0 k ) m For finding angle we will use dot…

Q: Find the cross product A x C for (a) A = 2.01 - 4.0j +k and C = 3.0i + 4.0j + 10.0k, (b) A = 3.01 =…

A: 1 )A→ = 2i^ - 4j^ + k^C→ = 3i^ + 4j^ + 10k^

Q: Given a force F that has magnitude of 240 N, find the angles ex, Oy, 0z that define the direction of…

Q: A (-3; 2; 0), B (0; 0; 6), C (2; -3; 0) and D (0; -3; 0), Since FBA = 152, FBC = 201 and FBD = 192,…

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

Q: Two points in the xy plane have Cartesian coordinates (5.50, -7.00) m and (-6.50, 6.50) m. (a)…

Q: Wector A lies in the XY plane and makes an angel 0 with the positive x-axis. if the y-component of…

Q: the x component of 40 m, 32° west of north? a. 40 m tan 32° b. 40 m sin 32° c. 40…

Q: Find the cosine of the angle between vector R= 4.3î + 2.1ĵ+7.3k and the positive direction of…

Q: 3 = 37 + 4ĵ +5k and M = 31 +4ĵ +5k js; The angle made by the two vectors

Q: A - 10.0 at 30.0° above the +x-axis; B - 12.0 at 60.0 ° above the +x-axis; and C - 15.0 at 50.0°…

Q: Consider the curve described by the parametric equations x = 3 cos t, y = 2 sin t. Compute the slope…

Q: Let B = 4.80 m at 60.0°. č and A have equal magnitudes. The direction angle of å is larger than that…

A: Magnitude of B is 4.80 m Angle of B is θB=60∘ Difference of angle of C and A is θC-A=25∘ Magnitude…

Q: From the table below, find the resultant (magnitude and direction) of J and D. A = 15 at 270°…

Q: Let B = 4.80 m at 60.0°. č and A have equal magnitudes. The direction angle of č is larger than that…

Q: 1.45 • Find the angle between each of these pairs of vectors: (a) Ả = -2.00î + 6.00oĵ and B = 2.00î…

Q: a heavy piece of machinery is raised by sliding it a distance d = 12.5 m along a plank oriented at…

Q: Two points in the xy plane have Cartesian coordinates (2.50, -6.00) m and (-4.50, 4.50) m. (a)…

Q: Find the sum of two vectors A and B lying in the xy plane and given by A = (2.01 + 2.0j) m B = (2.0î…

Q: V= (62.2 g +247.1g) / (62.2 g) * (V (2 * 9.81 * 0.011 m )) what is the unit of V = 0.310 %3D

Q: Find the x- and y-components of = 2A − B if A has components Ax = 15.0 m and Ay = 12.0 m whereas B…

A: Ax = 15.0 m Bx = 24.0 mAy = 12.0 m By = 8.00 m.C→ = 2A→ -B→…

Q: Find the cross product A x C for (a) A = 2.0i – 4.0j +k and C = 3.0i + 4.0j + 10.0k, (b) A = 3.0i =…

Q: Two points in the xy plane have Cartesian coordinates (5.50, -7.00) m and (-6.50, 6.50) m. (a)…

Q: A- 10.0 at 30° above the +x-axis; B = 12.0 at 60° above the +x-axis; and C - 15.0 at 50 ° below…

Q: A particle moving in a horizontal cirele of radius 0.5 m hns a speed 12 m s-1. Theangular speed of…

A: The speed of rotational motion is expressed through angular speed. It is the rate of rotations or…

Q: If S = (1 m) i + (2 m) j + (2 m) k and T = (3 m) i + (4 m) k, the angle between the two vectors a)…

Q: Given these vectors: A = (-7.3)î + (3)3+ (5.4)k B = (6.6)î + (3.5)j + (6.1)k č = (-1,7)î + (2.8)ĵ +…

Q: Let z(t) = t - sin(t) and y(t) = 1- cos(t) All answers should be decimals rounded to 2 decimal…

Q: Two unequal masses m1 and m2 are suspended from different points on a meterstick in rotational…

A: Given:

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: Given these vectors: A = (-4.8)î + (-2.7)ĵ + (6.4)k B = (-5.6)î + (-7.7)ĵ+ (9)k Find the value of…

Q: Two points in the xy plane have Cartesian coordinates (3.50, –5.00) m and (-6.50, 6.50) m. (a)…

A: Given: The coordinates of the points are 3.50, -5.00 and-6.50, 6.50

Q: Consider two vectors A= 6.75 i+(-3.53 k) and B= (-4.1j)+1.08 k. Find the angle between these two…

Q: The angle between A and B when A.B = 0 is a. 0 c. T/2 b. π/ d. t/6

Q: Given vectors: A = 8.3i + 33 and B = 6.5i + 7.4) Find AXB

Q: show that the vectors A= 1/2 q1+ 1/2 q2+1/2 q3+ 1/2 q4 and B= 1/2 q1 - 1/2 q2 + 1/2 q3 - 1/2 q4 .…

A: Dot product is defined as: A⇀.B ⇀ = ABcos(θAB) The dot product of orthogonal vectors is 0, since the…

Question

Show that the linear combinations h₁ = s + p_x + p_y + p_z and h₂ =
s − p_x − p_y + p_z are mutually orthogonal.

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

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

For what values of a are the vectors A = 2ai − 2j + ak and B = ai + 2aj + 2k perpendicular?
What is the magnitude of a→×(b→×a→) if there is an angle φ = 23.0° between the directions of a→ and b→? Assume a = 7.9 and b = 5.1.
Given that vectors T = + 2.00x + 6.00y – 4.00z and D = 2.00x – 3.00y – 4.00z The angle between the two vectors T and D is
If S = (1 m) i + (2 m) j + (2 m) k and T = (3 m) i + (4 m) k, the angle between the two vectors a) it's arcades (11/15) b) it cannot be calculated because S and T are not on the same plane. c) is arccos (11/225) d) is arccos (104/225) e) it's arcades (14/15)
Consider the two vectors, A=17x+11.5y, B=4.5x-3.5y. What is the angle of the vector A-B, measured counterclockwise in degrees from the positive x-axis?
A particle undergoes three consecutive displacements d1=(1.5i+3.0j-1.2km) cm, d2=(2.3i-1.4j-3.6k) cm and d3=(-1.3i+1.5j) cm. find the component and its magnitude.
Show that the force vectorD ⃗ = (2.0i ^ − 4.0j ^ +k ^ )N is orthogonal to the force vector G ⃗ = (3.0i ^ + 4.0j ^ + 10.0k ^ )N .
I kept doing the calculation in the calculator and wasn't getting the correct answer, can you help? two points are given in polar coordinates by (r, ?) = (2.20 m, 50.0°) and (r, ?) = (3.00 m, −60.0°) , respectively. What is the distance between them?
Two points are given in polar coordinates by (r, θ) = (1.80 m, 50.0°) and (r, θ) = (4.00 m, −40.0°) , respectively. What is the distance between them?
The Cartesian coordinates of a point in the xy plane are (−3.3, −3.8). Find the polar coordinates of the point (the radius and theta in degrres counterclockwise from the x axis.)
GIVEN: A = 3.0i + 4.0j + 2.0k B = 5.0i + 2.0j C = 2.0i + 3.0j Find A x (BxC)
If A = 4i − 3k and B = −2i + 2j − k, find the scalar projection of A on B, the scalar projection of B on A, and the cosine of the angle between A and B.