Final answer:
Vectors v and w are orthogonal.
Step-by-step explanation:
To determine whether vectors v and w are parallel, orthogonal, or neither, we can use the dot product.The dot product of two vectors v and w is given by the formula: v · w = |v| · |w| · cos(θ), where |v| and |w| are the magnitudes of v and w, respectively, and θ is the angle between them.If the dot product is equal to zero, then the vectors are orthogonal. If the dot product is equal to the product of the magnitudes, then the vectors are parallel. Otherwise, the vectors are neither parallel nor orthogonal.In this case, v = 3i - 7j and w = 6i + 18/7j. The magnitudes of v and w are |v| = √(3² + (-7)²) ≈ 7.62 and |w| = √(6² + (18/7)²) ≈ 7.95.The dot product of v and w is v · w = (3)(6) + (-7)(18/7) = 18 - 18 ≈ 0.Since the dot product is equal to zero, v and w are orthogonal.