Final answer:
To find the angle between vectors A = 3i + 4j + 5k and B = 3i + 4j - 5k, we use the dot product. The dot product is 0, which means the vectors are orthogonal to each other, and therefore the angle between them is 90°.
Step-by-step explanation:
The angle between two vectors A and B is calculated using the dot product formula and the magnitudes of the vectors. Specifically, if vectors A = 3i + 4j + 5k and B = 3i + 4j - 5k are given, the dot product A · B is calculated by multiplying their corresponding components and adding them together:
A · B = (3)(3) + (4)(4) + (5)(-5) = 9 + 16 - 25 = 0
Since the dot product is zero, this indicates that the angle between the vectors is 90°, meaning the vectors are orthogonal (perpendicular) to each other. Hence, the correct answer is A. 90°.