In our index notation a, b and cem represent a vector, a one-form and a 2) tensor in some cartesian coordinate system. as usual, the metric tensor is denotecd for each of the following geometric objects represented in index notation, identify the free indices, how many components the object has and what kind of tensor it is. b) gb d) a'b, a) a'b e) gkbcim 2. (10 points) relative to a specific coordinate system (the home system), evaluate the numerical value of each of the components of the geometric objects of problem 1 if the components of the vector, one-form and (tensor are a12 c11 2 c12-3 c13-1 c312 c324 c332 3. (15 points) the rotation transformation coefficients for a rotation from the home coordinate system of the previous problem to an other frame are 0.6 0.8 0 r0.8 0.6 0 the rotation is through an angle of a bit more than 53° about the z axis. determine the numerical values of the components of the vector, one-form andtensor of the previous problem. 4. (10 points) if the transformation coefficients of the rotation described in the previous problem are correct, what are the inverse transformation coefficients, r. to check r answer, show by direct calculation thata ar for any vector a