it's me again lol. I was trying to solve the problem below:
My answers in (b) matches with the answers in the answer key but the angle given for (c) in the answer key is 54.6 degrees while my answer was 125.39 degrees. I noticed that in the answer key, the component form of Earth was used as negative values while solving for the dot product, thus, yielding a positive dot product while mine was negative, -0.97. I really can't wrap my head around why negative values were used instead and would really appreciate if someone could explain that. Additionally, in the answer key, (d) states that Mars could not be visible at midnight, because the Sun-Mars angle is below 90 degrees. May I ask why is that not visible?