The force acting on a particle is given by  F(r) = (A/r2)r̂,  where A is a positive constant. (a) What are the dimensions of A?   Can the force be negative?   (b) Sketch F versus r. (c) Find the work done by the force on the particle as it moves from  ri = r0 to rf = 5r0.  (Use the following as necessary: A, r0.)   (d) Check your answer by comparing it with the case of a particle moving under the influence of gravitational force near a planet.

Q: If the scalar product of two vectors, A and C, is |Ã| - equal to -3.5, if two vectors when they are…

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Q: Use the definition of scalar product, á · b = ab cos 8, and the fact that á · b = abx + a,by + azb,…

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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→

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Q: If A=3i+7k and B= -1+2j+k. What is the angle between vectors A and B ?

A: The dot product of the two vectors can be calculated as,

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A: Given: Magnitude of a vector a is |a| =17 units Magnitude of second vector b is |b| =5.5 units and…

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Q: The scalar product of two vectors, A and B, is –7.5. If vector A is given by (3i - 4j) and the…

A: Given : Scalar product (A . B) = -7.5 Magnitude of Vector B (  |B| ) = 4.0 Finding the Magnitude of…

Q: Two vectors in Cartesian coordinates have components A= (2,2,3) and B=(-4,-1,7). What is the dot…

A: given  A=2,2,3  B=-4,-1,7  Dot product of vector  A with vector B=?

Q: Use the definition of scalar product, a b =ab cosθ, and a b =ax bx + ay by to calculate the angle in…

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Q: Using the definition of scalar product, calculate the angel between the two vectors given by à =…

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Q: If vector A has a magnitude of 5N, vector B has a magnitude of 7m, and the angle between vectors A…

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Q: ) Suppose u = (–3, –5,0), i = (0, –5, 1), and w = (1,5, 5). Compute the three triple scalar products…

A: Given: u→=-3i^-5j^+0k^v→=0i^-5j^+1k^w→=1i^+5j^+5k^

Q: USING THE PRODUCTS OF VECTORS. The scalar product of vectors Å and B is +48.0 m². Vector Å has…

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Q: In this problem we are going to consider two different examples of the dot product between two…

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Q: "If vectors A = 4i + 3j + 2k and B = 2i + 3j + 4k, then the dot product A.B will be equal to"

A: Given vectors A = 4i + 3j + 2k B = 2i + 3j + 4k To find dot product, A.B

Q: 1.41 For the vectors A, B, and C in Fig. E1.22, find the scalar pr ucts (a) A B; (b) B-C; (c) A. C.…

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A: Cross product: Cross vector of two vectors A→and B→ is given as, A→×B→=i^j^k^AxAyAzBxByBz where Ax,…

Q: The scalar product A · B of the two vectors A = 2i + 3j and B = i - 2j is O 8 k O -4 k O 2i - 6j

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Q: A mass of 76g is placed on the end of a 3cm vertical spring. This causes the spring to extend to…

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Q: Find the angle between the two vectors À=2î+3 ĵ +& B=-4î+2ĵ–k

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Q: "If vectors A = 3i + 4j + 5k and B = 2i + 3j + 4k, then the dot product A.B will be equal to" 38 28…

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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: For the vectors A=-21i+21j and B=7i+23j find the result of the dot product A.B Select one: 553.0 O…

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Q: find (a) 2u + v and (b) 5u - 2v.

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Q: Why is the following situation impossible? A barge is carrying a load of small pieces of iron along…

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Q: If A C =-11.1, A = 3i -43, and C= 6.5, the angle between the two vectors when they are drawn…

A: The dot product of the two vectors is  A→ . B→ = A B cos θ where, θ is the angle between the two…

Q: If A = iAx + jAy + kAz and B = iBx + jBy + kBz, show that the scalar product of A.B = AxBx + AyBy +…

A: Given that A = iAx+jAy+kAzB = iBx+jBy+kBz

Q: Chapter 09, Problem 007 In the ammonia (NH3) molecule of the figure, three hydrogen (H) atoms form…

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Q: The vector product of vectors A and B has magnitude 20.0 m² and is in the+z-direction. Vector A has…

A: The vector form of the vector A can be given as, The vector form of the product of the vectors A…

Q: Calculate the dot product:          A ∙ B,  given that vectors A = 3i + 6j a nd B = 4i – 4j

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Q: Vector C has magnitude 6.50 and is at an angle of 55.0° measured counterclockwise from the +x-axis…

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Q: Vectors A and B have scalar product -7.00, and their vector product has magnitude +9.00. What is the…

A: Express the scalar product of vectors A and B. A·B=ABcosθ-7.00=ABcosθ ---1 Here, θ is the angle…

Q: Find the work performed when the given force F is applied to an object, whose resultingmotion is…

A: Given:-the force is in pounds and the displacement is measured in feet.  F→=13j^d→=44i^ Find:-  the…

Q: Given two vectors A=4.00i + 7.00j and B=5.00i - 2.00j. Find the scalar product and vector product of…

A: The given values are, A=4.00i^+7.00j^B=5.00i^-2.00j^

Q: Evaluate the double integral Suppose we change the order of 1 x2 + 3x + 4y dx dy : integration in…

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Q: Given two vectors Á = 4î + 3j and B = 12î – 5j a)Find the scalar product A · B. b)Find the angle…

A: (a) The scalor product of the given two vectors can be calculated as,

Q: Find the scalar product of two vectors : A=3i+4j+5k B=2i-3j+6k

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Q: If v×w =2i −3j+2k, v×w=2i−3j+2k, and v⋅w=5, and θ is the angle between v and w, then

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Q: 1.47 •• The vector product of vectors Á and B has magnitude 16.0 m² and is in the +z-direction. If…

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Q: Given that vector u has length 3, vector v has length 5, and the dot product of u and v is -1, what…

A: Given:- length of u=3,            length of v=5   the dot product of u and v  = -1  now…

Q: The dot product of the same vector to itself is magnitude of the vector O Infinity square of…

A: as per guideline I m solving the first one we know that a.b=abcosθ

Q: Problem 20:  Assume you have two vectors, A = 7.1i + 3.9j and an unknown vector B with length 3.2.…

A: Assume you have two vectors, A = 7.1i + 3.9j and an unknown vector B with length 3.2. In this…

Q: ectors A and B are given by: A = 24.15i + 22.01j B = 80.63i + 23.67j Find the scalar product…

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Q: Problem 20:  Assume you have two vectors, A = 7.1i + 3.9j and an unknown vector B with length 3.2.…

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Q: If vectors A = 4i + 3j + 2k and B = 2i + 3j + 2k, then the dot product A.B will be equal to... "

A: Solution as

Q: Two vectors A and B in two dimensions are given by A = 2i + 3j and B = - i + 4 Find the magnitudes…

A: Let us solve this question step by step :-Given that ,A→=2i∧+3j∧ and B→=-i∧+4j∧so , magnitude of…

Q: Vector A has magnitude 6.0 m and vector B has magnitude 12.0 m. If the scalar product of these two…

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