###### Question:

Please write the answer to all 4 uploading problems including this one on the paper and upload the answer in one pdf file after you finish and submit this final. [13].: - [] (9 points) Letü Recall that each vector correspond to a point in R2 (a). (3 points) Show that the triangle with vertices ő, ü, ö is a equilateral triangle (ie. a triangle with equal-length sides). What is the length of the three sides? (Hint: the third side can be expressed by vector ü - 7.) (b). (3 points) Show that {ü + jöis the height of this triangle w..t. the third side. i.e. show that yü + Lüis orthogonal to ü - . (c). (3 points) Can you find a pair of vectors ā, 6 s.t. the triangle with vertex o, a, b is a equilateral triangle with side-length 1?

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