Please anser item a and b. Examples are also attached for your reference.

\fa. Write the equation a = (a1 )2 + (b1 )2 + 2a1b1 + (a2)2+ (b2)2+ 202b2 + (a3)2+ (b3)2+ 2a3b3 in indicial and Gibb's notations. b. Let the scalar field f = f(X1, X2, X3) where 1 = 21(21, Z2, 23), 12 = 12( 21, 22, 23), and T3 = 13(21, 22, 23). Determine the first partial derivatives of f with re- spect to z; and express the results in indicial notation.Example 3. Express the following equation in indicial notation: w = [(a1)2 + (a2)? + (a3)?] (ci b' + c2 b? + (3 b3 ) Solution w = [(a1)2 + (a2)2 + (23) ?] (ci b' + (2 b2 + (3 b 3 ) = (ala1 + aza2 + a3a3) (C1 b + (2 b2 + (3 63) = aja; Ck bk