Consider the metric ds² = -y'da² + a³dy2. The component of the Riemann tensor Rayz is given by: Select one: 3 01. - Ay O 2.-3+2y² O 3. 0 04.-23+2

Q: Let a = (-3, –4, –4) and b = (2, 2, 4) . Find scalars s and t so that sa + tb = (20, 4, 32) %3D %3D

A: We have to find the values of scalers s and t for a=-3,-4,-4 and b=2,2,4.

Q: solve y(4)-3y'''+2y''=e3x  using undetermined coefficient

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Q: Express the vector below in Cartesian coordinate: B = 2r sin cosc a₁ + r cose cose aer sind a ax=…

A: Given: The vector, B=2rsinθcosφar+rcosθcosφaθ-rsinφaφ   To express: The given vector in cartesian…

Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: Find u · v. u - (7, 2) - (-6, 3) V u.v -

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: what are the examples of contravarient and covariant tensors?

A: Example of Covariant tensor: A'i=aijAj

Q: If A and B are both second-order tensors and t, u, v, and w are all vectors, prove the following…

A: Given that if A and B are both second-order tensors and t, u, v, and w are all vectors.   (1). To…

Q: Calculate the triple scalar products w. (vx u) and u (w x v), where u = (7, 2, -1), v = (2, 8, -3),…

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Q: Can a vector in a vector space R -4 - 2 be 2. span by -1 2 イ

A: Span of vectors.

Q: Select the option that gives the vector product of i+k and i + j Select one: 01 Oi+j-k Oi-j-k…

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Q: What conditions on a column vector u will make ulu zero? T

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Q: Find the coordinate vector [x]B of the vector x relative to the given basis B. 23) b1 =| b2 and B =…

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Q: let R = (-2, 7). Calculate the following: The components of u = PŔ, where P = (1, 2)

A: Given,               R=(-2, 7)   and   P= (1, 2).    The components  of u=PR⇀=?

Q: Find the unit vector in the direction of v = (3, 5).

A: It is given that, v→=(3,5)   It is known that a vector R→=ai^+bj^ can be written as, R→=(a,b). As we…

Q: Let X=(1,-3)t be the transpose of vector (1,-3). If you rotate X by angle of π/3 what are the…

A: The transpose component is X=1, -3t

Q: . Prove that there is no distinction between contravariant and covariant vectors if the…

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Q: If T is a mixed tensor, then T} + T{ is generally not a tensor a tensor May or may not

A: Answer : may or may not  Hence, Option (iii) is true.

Q: Identify the type of answer that results from each operation (vector or scalar). If the operation is…

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Q: Let z = 6. and y Find the vectori = 47 - 7j and its additive inverse.

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Q: Find the unit vector having the same direction as i = ( – 1,9). V82 V82, 9. of- 1 9. V82 V82 O (1,…

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Q: If ï = (, 2), find a vector i that is perpendicular to ū.

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Q: The functions g(b, c, d) and h(b, c, d) are defined as: g = (b+ c+ d')' + (b' + c' + d') · (b' . c'…

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Q: 5. Drop a vector from the set A {sin'x,-1,1, sin 5x} to make it independent in F(-00, 00)

A: A set is linearly independent if no vector can be written as linear combination of others.

Q: 1) S-4 5²-85+ 10

A: