We have a - b = -i + j + k
c - b = i + 3j + 5k
(a - b) × (c - b) = | i j k | | -1 1 1 | | 1 3 5 | = 2i + (-5 - (-1))j + (-3 - 1)k = 2i - 4j - 4k
The required unit vector is:
(a - b) × (c - b) / |(a - b) × (c - b)| = (2i - 4j - 4k) / √(2² + (-4)² + (-4)²) = (2i - 4j - 4k) / √36 = (2i - 4j - 4k) / 6 = (1/3)i - (2/3)j - (2/3)k