If u and v are any vectors in R2, show that ||u + v||2 < (||u|| + ||v||)2 and hence l|u + v|| < ||u|| + ||v||. When does equality hold? Give a geometric interpretation of the inequality.

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If u and v are any vectors in R2, show that ||u + v||2 < (||u|| + ||v||)2 and hence l|u + v|| < ||u|| + ||v||. When does equality hold? Give a geometric interpretation of the inequality.