Science:Math Exam Resources/Courses/MATH152/April 2022/Question A02

MATH152 April 2022

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Question A02
Consider the two vectors ${\vec {OA}}=[-4,2,4]$ and ${\vec {OB}}=[-6,3,2]$. What is the circumference of the triangle OAB? (The circumference, also known as the perimeter, is the sum of the legths of the three edges.) Triangle with vertices O, A, B.

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
The third side of a triangle is a linear combination of the other two sides.

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Solution

Found a typo? Is this solution unclear? Let us know here. Please rate my easiness! It's quick and helps everyone guide their studies. We have ${\vec {BA}}={\vec {OA}}-{\vec {OB}}=[2,-1,2].$ Therefore, we may compute the side-lengths of the triangle OAB: $${\begin{aligned}\|{\vec {OA}}\|&={\sqrt {4^{2}+2^{2}+4^{2}}}={\sqrt {36}}=6\\\|{\vec {OB}}\|&={\sqrt {6^{2}+3^{2}+2^{2}}}={\sqrt {49}}=7\\\|{\vec {BA}}\|&={\sqrt {2^{2}+1^{2}+2^{2}}}={\sqrt {9}}=3\end{aligned}}$$ In conclusion, the circumference of the triangle is 6+7+3 = 16.