UNIVERSITY OF CALIFORNIA BERKELEY Structural Engineering,Department of Civil Engineering Mechanics and MaterialsFall 2000 Professor: S. GovindjeeHW #2: CE231 / MSE211As we have seen we can express vectors in terms of their components with respect to aparticular basis. Thus we can writev = viei. (1)When the particular basis is understood (ie. everyone reading the equation will assume thesame basis) one can safely express the components of the vector in a “column vector”; ie. asvi→v1v2v3. (2)This convention also applies to second order tensors. In this case we have for a basis e ={e1, e2, e3}T = Tijei⊗ ej. (3)If the basis is understood we can express the components in a 3 × 3 matrix. The followingordering is conventional:Tij→T11T12T13T21T22T23T31T32T33(4)For the problems assume an orthonormal basis e = {e1, e2, e3} anda = 2e1+ 5e2− 7e3, (5)b = 0e1− 8e2+ 1e3, (6)ci→457, (7)andTij→1 8 28 3 22 2 3. (8)Find the following. Express your answers in dyadic and matrix/column vector form (assumethe e basis). When the answer is a scalar, just give the number.1. (a · b)c2. b3a · c13. (a · b)a ⊗ b4. δii5. T3jδ3j6. Tijδij7. TijTij8. T c9. IT10. IIT11. IIIT12. e1⊗ e213. e3⊗