Define and give three examples of contravariant and covariant tensors ?

Q: Define the term binormal vector?

A: Question:- Define the term binormal vector?

Q: Find the magnitude of vector v. 1 X + + 1 2 4 (4,-3) -2+ -3+ -4 -5 - ليا 3 5

A: To find the magnitude of the given vector v .

Q: Given that p and r find in column vector form:

A: In this question, we find the column vector by using the given vectors.

Q: What is the relationship between vector subtraction and the basic vector operations of addition and…

A: What is the relationship between vector subtraction and the basic vector operations of addition and…

Q: vector v is multiplied by the scalar -, the resulting vectór 4' smaller than v and in the same…

A:

Q: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

A: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

Q: Find the length of the vector. v = (0, 2) ||v| = %3D

A:

Q: What is meant by scalar multiple?

A: Let V be a vector space over the field ℝ. Take u,v ∈V.

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

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

Q: e diagonalizable?

A:

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: Suppose that r1(t) and r2(t) are vector-valued functions in 2-space. Explain why solving the…

A: It is given that r1(t) and r2(t) are vector valued functions in 2-space. The objective is to explain…

Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: Give an example to show that vectors are not commutative under the cross product operation. Justify…

A: The objective of the question is checking the commutative fail in vector cross product.

Q: Find T, N, B,

A: Note:- As per our guidelines, we'll answer the first three sub-parts of this problem as exactly…

Q: 5. i ',, Find the solution space and write it as a linear combination of vectors. - x3 + 5x4 X2 +…

A: Given that x1-x3+5x4=0 x2+4x3-3x4=0

Q: How do you know if 3 vectors span R^3? Is there any example?

A:

Q: Explain the term scalar.

A: Explanation: Given that, term scalar.

Q: Let W1 and W2 be skew-symmetric tensors with axial vectors w1 and w2 respectively. Show that…

A: To prove this identity we will use an identity. Proof of that identity is given below:…

Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: Find the length of the vector x=x= |x|=|x|=

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Q: orthogonal.

A:

Q: By using vector scalar multiplication and vector triple product, prove the identity below: Ã x [Ã x…

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Q: If a vector is expressed in terms of i and j, explain how to find the scalar multiplication of the…

A: The vector quantity has both magnitudes as well as the direction. if we multiply a vector by a…

Q: Find the Values of for which vectors linearly dependent the are -3 4 -5 8. 6. - 2 6. -8

A: Given that three vectors are linearly dependent.

Q: Two vectors are equivalent if they have the same _______ and _________.

A: Two vectors are equal if they have same magnitude and same direction. If we have a vector u=3i+4j…

Q: What is the determinant formula for calculating the cross product of two vectors relative to the…

A: Consider two vectors relative to the Cartesian i, j, k-coordinate system.

Q: What is the effect of scaling a Vector? Give an example?

A: we need to explain the scaling of vector. and we  need to give an example. First let us define what…

Q: If the components of a contravariant tensor in x' coordinate system are (8,4). Show that its…

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Q: what is the linear combination of  u⃗  and v⃗ ?

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Q: If the components of a contravariant tensor in x' coordinate system are (8,4). Show tha its…

A:

Q: The amount of money currently in your bank account is an example of a vector. O True False

A:

Q: Define the term vector.

A:

Q: 3 Compute the length of the vector v =

A:

Q: е. (а-Б) х (а-d) f. (ä x5) · (č x đ)

A: Given query is to find which is meaningful an which is meaningless.

Q: Define the term column vector.

A: Column Vector is defined as a column matrix representing the elements of any vector written in…

Q: Proivde Definitions of Vectors and Matrices?

A: Vector: A vector is a group of numbers whether it is in row or in column. vector is also a matrix.…

Q: orthogonally diagonalize A

A:

Q: Determine the resultant of the force system in the figure.

A: In this question we use the given figure for forces to find the magnitude of the forces

Q: If A is second order tensor ,then ylgn O ihi O

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Is Vector Y in the Column space of A? What is the solution set? Write y as an appropriate linear…

A: the vector y is in the column space of A is the system Ax=y is consistent 819-59-13108abc=123…

Q: If A is second order tensor, then

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Find a unit vector

A:

Q: fintuint vectorfor3atb if ã-2i+4 + k b=i-2i-3K

A: The vector of r can be computed by substituting the value of a and b in the given expression and…

Q: The number of elements in a vector generated by [4:0.1:13] is

A: We have to find the number of elements in a vector generated by  [4 : 0.1 : 13].

Q: Find the vector, not with determinants, but by using propertles of cross products. (1 x ]) x k Watch…

A: Cross products property i x j = k           eq(1) j x k= i k x i= j And i x i=0 , j x j=0 and k x…

Q: (Ъ) (aU) · (bV) = ab(U.V)

A: Explanation of the answer is as follows

Q: Express the product Ax as a linear combination of the column vectors of A. 1 21 3 + 3 +3 2.

A: The given product, A2×2x2×1=12-3432 Which will result into a vector of order 2×1

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.