Answer: The answer is 3.75 and -2.5.
Step-by-step explanation: We are given to find the values of b and c if the vector (5, b, c) is orthogonal to (1, 2, 3) and (1, -2, 1).
We know that if two vectors are orthogonal, then their dot product is equal to zero. So, we have

and

Adding equations (A) and (B), we have

and from (B), we have

Thus, the value of b is 3.75 and the value of c is -2.5.