Science:Math Exam Resources/Courses/MATH152/April 2013/Question B 02 (b)
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Question B 02 (b) 

Let , and . Let be the triangle whose vertices are A,B, and C. Prove that is a rightangled triangle. 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

There is a relationship between the dot product of two vectors and these vectors being orthogonal, do you know what it is? 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let
and let
as in part (a). The vector are orthogonal if their dot product is zero. Calculating this dot product yields
Thus, vectors and are orthogonal and so the triangle is right angled. 