Final answer:
The vectors 2i - j + 4k and 5i + j - 2k are not orthogonal.
Step-by-step explanation:
To show that two vectors are orthogonal, we need to demonstrate that their dot product is zero. Let the first vector be a = 2i - j + 4k and the second vector be b = 5i + j - 2k. The dot product of a and b is given by a · b = (2)(5) + (-1)(1) + (4)(-2) = 10 - 1 - 8 = 1. Since the dot product is not equal to zero, the vectors a and b are not orthogonal.