Final answer:
The length of one side of the rhombus is √26 units.
Step-by-step explanation:
To find the length of one side of the rhombus, we need to find the magnitude of the given vectors 3i-4j-k and 2i+3j-6k. The magnitude of a vector can be found using the formula: |A| = √(Ax)² + (Ay)² + (Az)².
For the first vector 3i-4j-k, the magnitude is |A| = √(3)² + (-4)² + (-1)² = √9 + 16 + 1 = √26.
For the second vector 2i+3j-6k, the magnitude is |B| = √(2)² + (3)² + (-6)² = √4 + 9 + 36 = √49 = 7.
Since a rhombus has equal side lengths, the length of one side of the rhombus is equal to the magnitude of these vectors, which is √26 units.