The problem involves determining whether triangle ABC, defined by the vertices A(4, 1, 7), B(-2, 1, 1), and C(-3, 5, -6), is a right triangle. The discussion centers around the use of vector mathematics and the properties of the dot product in relation to the triangle's sides.
Participants are exploring different methods to determine the nature of triangle ABC. There is a recognition that the dot product calculations do not indicate a right triangle, but the conversation reflects a lack of consensus on the best approach to confirm this conclusion.
There is mention of confusion regarding the calculations of the vectors and their dot products, as well as the need for clarity in notation and presentation of work. Participants are also checking the accuracy of the problem statement and their calculations.
justsof said:I think it is the right approach, but ask yourself; why are you using the dot product? Is there a property of the dot product that you can use? And what does it mean if this product is zero?
Mark44 said:You should be using the vectors that represent the sides of the triangle. What you have found is that the vectors to vertices A and B happen to be perpendicular, but that doesn't say anything about the sides of this triangle.
Don't put anything like the above in your work that you hand in, since it's gobbledy-gook. I believe you know what you're doing in this problem, and I understant what you mean, but you're not writing what you mean. You don't have to say "using the formula ..." Your instructor understands how to get the vector that joins two points.spoc21 said:using the formula [(b1-a1), (b2-a2), (b3-a3)] so [(-2-4), (1-1), and (1-7)]
[-6,0,-6]