For what values of a, b are the vectors (1, 1, a)^T and (b,−1, 1)^T orthogonal
(a) With respect to the dot product?
(b) With respect to the weighted inner product of Exercise 3.2.17?

Data From Exercise 3.2.17

Answer Exercises 3.2.15 and 3.2.16 using the weighted inner product (v ,w) = 3ν₁ω₁ + 2ν₂ω₂ + ν₃ω₃.

Data From Exercise 3.215

(a) Find a such that (2, a,−3 )^T is orthogonal to (−1, 3,−2)^T. 

(b) Is there any value of a for which (2, a,−3)^T is parallel to (−1, 3,−2)^T?

Data From Exercise 3.2.16

Find all vectors in R³ that are orthogonal to both (1, 2, 3)^T and (−2, 0, 1)^T.