If dS2 = gij dxi dxj is invariant, then which of the following is true?

If Aij ≠ 0 are the components of a tensor of type (0, 2) and if k Aij + k1 Aji = 0, then which of the following statements is false?

For a three-dimensional coordinate system (x1, x2, x3), the components of the unit tangent vector along the x1-curve are given by: