2.53 Prove the following identities when A and B are vectors and S, R, and T are second- order tensors: (a) tr(AB) = A.B. tr(ST) = tr S.

Q: If a = i+ 3j +k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A:

Q: A force is specified by the vector F = [(-170)i + (120)j + (-80)k] N. Calculate the angles made by F…

A:

Q: Find unit vectors that satisfy the given conditions: 1. The unit vector in the same direction as…

A:

Q: MNPQ is a parrallelogram and R is the intersection point of the diagonals MP and NQ. Let vector U =…

A: Step 1:parallelogram law -MP=MQ+QP=u+vand NQ=MQ+MN=u+v Step 2:…

Q: Let u, v be unit vectors and c ∈ R be a scalar. Use the fact that Dvg(a, b) = ∇g(a, b) · v to show…

A:

Q: find the component form of the e resultant vector if₁ v= and w=. Find la v-swl.

A:

Q: Find the unit vector in the same direction as the vector u = [2, –1, –9]. Ex: 1.234 C Ex: 1.234 Ex:…

A: We will find the modulus (norm) of the vector and divide the vector by the norm to find the unit…

Q: For vectors ?⃗ = ⟨2, −3, −2⟩, ? = ⟨1, −4, 2⟩ Find the projection of vector ?⃗ onto the vector ?.

A:

Q: Let u and v be vectors in Rn. Show that 1 1 |||u + v||² − − ||u − v||² . - 4 u. V =

A: Given: u and v are vectors in Rn We are required to prove: u.v=14u+v2-14u-v2

Q: If a charged particle of charge q� is travelling with a velocity v� in a magnetic field B,�,  then…

A: The objective of this question is to find the direction of the force that a moving proton feels when…

Q: For any vector A,ix (i x A) +jx (j xA) + kx (k xA) = -2A ylan O İhi O

A: We use vector triple product to answer the given question.

Q: 12. Let A = ( d ef g h Find the column vector B such that AB =

A: Let A be a square matrix. Use the following formulae, to obtain the required result.

Q: Consider the vectors below. For this exercise you should round all answers to one decimal place. F₂,…

A:

Q: O Find a unit vector (a vector with length 1) that has the direction of 3 2

A: Given below the detailed solution

Q: tA= ate V x V x A forr 0. T Here a is a constant vect

A:

Q: What is the resultant of vector A=2i +3j. and vector B=3i -2j Select one: a. 3.5 O b. 2 C. 5/2 Od.…

A: A vector is something that has both magnitude and direction. Like, if you are saying, someone is…

Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: A. B. | Find a nonzero vector w € R³ which is orthogonal to u but not orthogonal to v Find a nonzero…

A:

Q: 4. [6.1] If vector b is shown below, sketch a vector. a) Equal to b b) Opposite to b c) With the…

A: Solution of given question is written in below steps.

Q: Q3. Prove that (only one): a-dy is a unit vector? a- %3! b- L = 6a, - 3a, + 2a, and M = 3a, + 2a, -…

A: Topic- Vector

Q: Use a change of variables to evaluate the integral (look at picture below for integral) where D =…

A:

Q: If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A: We have to find

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: -2 Let v be the vector 1 |. The vector of length 6 in the same direction as v is 2 Select one: 4 a.…

A:

Q: The vector w is a unit vector, and the vector i is any non-zero vector. If z = (x · W)w and ỹ = i –…

A: Use the property of dot product and associative and distribute property to solve the problem.