Final answer:
The y-component of the resultant vector R (Ry) is found by summing the y-components of vectors A and B, given by Ay and By. As per the calculations using Ry = Ay + By, the value of Ry, when AB is a straight line and given Ay = 12 and By = 15, is Ry = 27.
Step-by-step explanation:
The problem you are working with involves vectors and their magnitudes. Specifically, you need to find the value of y when AB is a straight line. The value of y for points A and B are given as Ay = 12 and By = 15, respectively. The notation Ry = Ay + By suggests that we are summing the y-components of vectors at point A and point B to get the y-component of the resultant vector R.
Using the Pythagorean theorem, R can be found by the equation R = √(Rx² + Ry²). The problem states that Ry = Ay + (-By) which indicates that vector By is in the opposite direction to Ay. However, since AB is a straight line, and provided values Ay = 12 and By = 15 are given without signs, it's likely these should be directly summed to find Ry.
Let's calculate Ry:
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- Ay = 12
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- By = 15
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- Ry = Ay + By = 12 + 15 = 27
Assuming then that Cy and Dy are not directly relevant to the problem as stated, we would conclude that the value Ry=27 when AB is a straight line given that Ay=12 and By=15. Please review the question to ensure all necessary information has been provided to solve for Ry accurately.