Prove that the scalar product of a relative covariant vector of weight w and a relative contravariant vector of weight w' is a relative scalar of weight w+w' .

Q: Prove that matrix multiplication is associative. Show that the product of two orthogonal matrices is…

A: The objective of the question is to prove two properties of matrices: the associativity of matrix…

Q: Find a vector of magnitude 8 in the direction of i = (-4, –6, –1). Vector is Find a vector of…

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Q: The unit vector from A(4, 2) to the point B(-2, 10) is:

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

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Q: Force F has coordinates of lbs and position vector r lies in the xz plane with components of ft.…

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Q: Scalar or dot product of vectors 9i + 6j + - 4k and 1i + 3j + 0k?

A: Solution: given that A = 9i + 6j + - 4k  B = 1i + 3j + 0k to find the dot product

Q: Given M  = 3 î + ĵ − 4k̂  and  N= 3 î − 4 ĵ −k̂ , calculate the vector product  M ✕ N.

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Q: There are two not orthogonal forces (F and F), if the resultant of these forces is also equal to…

A: Resultant of two force F1 and F2 is given by,  F=F12+F22+2F1F2cosθ Given both the forces are equal…

Q: A vector a of magnitude 17 units and another vector b of magnitude 5.5 units differ in directions by…

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

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: A vector a→a→ of magnitude 18 units and another vector b→b→ of magnitude 7.6 units differ in…

A: Given data:  Magnitude of the vector A = 18 units Magnitude of the vector B = 7.6 Angle between…

Q: If the vector Kâ- +Lây+ M â, shows the maximum increase rate and direction of the scalar V at point…

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Q: The scalar product of vectors A→ and B→ is +51.0 m2m2 . Vector A→ has magnitude 8.00 mm and…

A: Given: A.B=51 A=8.00 mm The angle θ=28° west of south. If B vector has direction 39.0° To determine…

Q: Vector u = <-7,3,-5> and vector v = <-1,1,0>. Find the cross product of u X v.

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Q: Given the following information, find the unit vector of Force A Force A = 200 N Θ = 30o (on x-y…

A: Given: Vector A : 200 N Angles θ=30∘ ( on x-y plane) ϕ=50∘ ( on x-z plane)

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

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Q: (a) Find the scalar products î î, ĵ· ĵ, and k · k. (b) Find î · î, î · k, and k î (c) Use the…

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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: Let vector a = and vector b = . The the cross product of vector a and b.

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Q: Find the cross product vectors A =i – 2j+ 3k and B = 2i + 3j - k

A: Given that:To determine the cross product of vectorsA=i-2j+3kB=2i+3j-k

Q: Given the pair of vectors, A = (9.0oî – 2.00ĵ ) and B = (-2.00î + 7.0oj ), use the definition of a…

A: A→ = (9i^ - 2j^) B→ = (-2i^ + 7j^)

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

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Q: Given the vectors = [(3.45 m)j + (1.75 m)k] and B = [(1.35 m)i + (2.25 m). What is the product BC?

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Q: Given M = 3 î + 4 ĵ – 4 k, and  N = î − 4 ĵ −  k, calculate the vector product  M x N

A: Given: M=3i+44j-4kN=i-4j-k

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

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Q: (c) Use both methods to calculate ā · b for each of the following cases: (i) if ā = (-4, –9) and b=…

A: Given data: (i) The coordinate of the vector is, a→=-4, -9b→=-1, 2 (ii) The magnitude of vectors and…

Q: Consider the vectors a = i + 8j + 4k and b = 7i − 6j − 6k, where i, j, and k are…

A: Given that: The vector a is a=i+8j+4k The vector b is b=7i-6j-6k   It is required here to calculate…

Q: One vector has magnitude 18 units and another 5.5 units. Find their scalar product if the angle…

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

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Q: a certain corner of a room is selected as the origin of a retangualr coordinate system. A fly is…

A: Write the given values with suitable variables. x=3.7y=1.3

Q: If A=- 2i+2j and B = -i+3j-2 k, find the scalar product of the vectors A and (-2A + 3B}?

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Q: Find 2 unit vectors orthogonal to both u = <4,-2,3> and v = <0,3,7>.

A: The objective of the question is to find two unit vectors that are orthogonal (perpendicular) to…

Q: Let vectors: A=(1,0,−3) B=(−2,5,1) and C=(3,1,1).   Calculate A×(B×C) Calculate A⋅(B×C)…

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Q: What is the dot product A•B if A = 2x - 3y and B = 15x + 10y?

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Q: Let vectors A⃗=(2,−4) A → = ( 2 , − 4 ) and B⃗=(−3,1) B → = ( − 3 , 1 ) . Calculate the following:…

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Q: Vector A has a magnitude of 4 m and lies in the xy plane directed at 45 degrees counterclockwise…

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