The distance of the plane 2x – 2y – z = 27 from the origin is A 9 B 3 C 27 D 6

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: Evaluate the volume between the surface z = 3 + 2x + xy, and the rectangle in the xy plane given by…

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Q: If k is any positive number, what is the size of the angle between the vectors a = (k, k) and b =…

A: The angle between the vector a→ and b→ is define by the following formula. cosθ=a→·b→a→b→

Q: 2.2 Express the following points in cylindrical and spherical coordinates: (a) P(1, –4, –3) (b) Q(3,…

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Q: A = (3, 5, -7) B = (2, 7, 1). Find A + B. A- B, A, B, A B, and the cosine of the angle between A

A: A→=3i^+5j^-7k^B→=2i^+7j^+1k^ A→+B→=3i^+5j^-7k^+2i^+7j^+1k^=5i^+12j^-6k^

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

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Q: "Vector, that's me!" Gru's position coordinates were locked at (x, y, z) = (10, –3, 15) [m] from…

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Q: M = -3î + 6j – 5k and N = -21 + 3j + k The cross product of MxN equals Choose the best answer. A -9i…

A: Given: M→=-3i^+6j^-5k^N→=-2i^+3j^+k^

Q: 1. Calculate the dot product of vectors a and b: 30.0 B (2.40 m) y 0 A (3.60 m) 70.0⁰ 2. Sam has…

A: 1.  Dot product between two vectors is given by, A'.B' = |A| |B| cos(theta)         = 3.6 * 2.4 *…

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

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Q: A sphere is placed over the three closely packed identical spheres on a horizontal plane. All the…

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Q: In the shown figure, the length of the side of the square is 2a , if q;=Q is placed at point "7",…

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Q: Suppose A = (-3.92 m)i + (3.66 m)j, B = (2.56 m)i + (-4.99 m)j + (2.05 m)k, and D = (-3.69 m)i +…

A: The vector A=-3.92i+3.66j. The vector B=2.56i-4.99j+2.05k. The vector D=-3.69i-3.85j.

Q: Problem 12: A merry-go-round is a playground ride that consists of a large disk mounted to that it…

A: Dear student When there is no external torque acting on the system, the angular momentum remains…

Q: Two vectors have the following magnitude, A = 11.6 m and B = 14.3 m. Their vector product is: AxB =…

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Q: Calculate the areas of the following surfaces using the differential surface area dS p=2,0 ≤z≤ 5,…

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

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Q: Show that the force vector B = 2î – 4ĵ + k is orthogonal to the force vector ở = 3î + 43 + 10k. [2]

A: There are Two vectors -

Q: What is the scalar/dot product of the given 3-dimensional vectors: A = (xy)i + (2yz)j + (3xz)k and B…

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Q: You have been given the points below (they are in the x-y plane). Figure the corresponding polar…

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Q: Problem 12: A merry-go-round is a playground ride that consists of a large disk mounted to that it…

A: To solve the given question, we will write down the moment of inertia of the merry-go-round…

Q: Find the point at which the line meets the plane. x = 1+ 6t, y = - 2+ 2t, z= - 2+ 5t; x+ y+z= - 3…

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Q: 1. The dimensions of gravitational constant are: (a) [M*£T*] (b) [M*LT=] [M'Er*] «d) [M*¢r*] (e)…

A: Solution:

Q: 1. The three vertices of a triangle are located at A(6, -1, 2), B(-2, 3, -4) and C(-3, 1, 5). Find…

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Q: In Problems 37 to 40, evaluate the triple integrals. -2x 37. dz dy dx 38. dy da dz 2=0 y=82 -2 2y+%3…

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

Q: d, = 2a/ + +P dz = 2a/R + +P d2 = a/2K + +P

A:

Q: You have been given the points below (they are in the x-y plane). Figure the corresponding polar…

A: in this question  we draw a figure i do not have a graph paper so i did on plane paper.

Q: Given: A= 5i + 4j + 6k lbm B= 2i + 4j + 9k kgm C= 20i + 20k N Find: A.) Angles of A in radians B.)…

A: Cross Product: the cross product is a binary operation between two vectors which itself results in a…

Q: Consider a triangle ABC with sides AB = 14.9 cm and BC = 9.7 cm. Angle ABC is 38.4 degrees. What is…

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Q: If A.C =-7.5, Ā = 31 – 4j, and |C| = 6.5, what is the angle between the two vectors when they are…

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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: 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 =…

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Q: 1 2 3 y 8 4 7 6.

A: The vector r from 1 to O is given by:

Q: Suppose A = (-2.28 m)i + (4.92 m)j, B = (2.69 m)i + (-3.81 m)j + (1.48 m)k, and D = (-3.56 m)i +…

A: Angle between vectors D and A is,

Q: What is the angle between vectors = 4+ 8 and Express your answer as an angle in degrees between 0 VD…

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Q: Problem 12: A merry-go-round is a playground ride that consists of a large disk mounted to that it…

A:

Q: Find the angle between vectors A = 3i – 2j and B = 4j – 4i using the definition of dot product. %3D…

A: Given data The equation of vector A is given as A→=3i^-2j^  . The equation of vector B is given as…

Q: Problem 6: A merry-go-round is a playground ride that consists of a large disk mounted to that it…

A:

Q: C = -3.0î + 4.0j , and and (d) C = -2.0 i +3.0 j +2.0k and Á =-9.0 j . 68. cross product A × Ć for…

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Q: Given vectors ū = [-2,3,1] i = [1,2, –2] and w = [4, –2, –1] find: b) ü w b) the angle between i and…

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Q: In the Bohr model of hydrogen atom, the n is pictured to rotate in a circular orbit of radius -11 m,…

A: An electric current is a stream of charged particles, such as electrons or ions, moving through an…

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

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Q: 1900 N 900 N 20 30 F25 70°

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Q: 6. Given vectors A = 2âz + 4ây + 10â, and B = –5âp + âs – 3âz, find %3D (a) Ã+ B at P(0, -2,5) ,…

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Q: Problem 6: A merry-go-round is a playground ride that consists of a large disk mounted to that it…

A: Hi, your question has multiple sub-parts so we will solve first three sub-parts for you. For…

Q: . Using the differential length dl, find the length of each of the following segments/curves: a) 2 <…

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Q: Suppose A = (-2.82 m)i + (4.13 m)j, B = (1.46 m)i + (-4.97 m)j + (1.68 m)k, and D = (-4.75 m)i +…

A:

Special Relativity

The theory of special relativity discusses how space and time are related to objects traveling along a straight line at a constant speed. Simply stated, as an object reaches the speed of light, its mass becomes infinite and it is unable to move faster than light. This interstellar speed limit has been the topic of much debate in astronomy, and also in science fiction when people consider how to fly over large distances.