Answer: ( 8, -11, -22)
Explanation:
As per the question, a rock climber's rope is supported with two anchors and one anchor can be represented by the vector a = -(-3, 5, 12) and the other anchor can be represented by the vector b= -(-5, 6, 10).
We need to find a single vector that can represent the sum of vectors.
To find the single vector that represents the sum of vectors, we need to add the two given vectors a and b. vector a = -(-3, 5, 12) = (3, -5, -12) vector b = -(-5, 6, 10) = (5, -6, -10)
Adding vectors a and b, we get: (3, -5, -12) + (5, -6, -10) = (8, -11, -22)
Therefore, the single vector that represents the sum of vectors is (8, -11, -22).
Hence, the correct answer is (8, -11, -22).