作业帮一道有关线性代数的题目（题目是用英语出的）For the vectors v=(3,4) and w=(3,4) test the Schwarz inequality on v·w and the triangle inequality on ||v+w||.Find cosA for the angle between v and w.When will we have equality |v·w|=||
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一道有关线性代数的题目（题目是用英语出的）For the vectors v=(3,4) and w=(3,4) test the Schwarz inequality on v·w and the triangle inequality on ||v+w||.Find cosA for the angle between v and w.When will we have equality |v·w|=||
一道有关线性代数的题目（题目是用英语出的）
For the vectors v=(3,4) and w=(3,4) test the Schwarz inequality on v·w and the triangle inequality on ||v+w||.
Find cosA for the angle between v and w.
When will we have equality |v·w|=||v|| ||w|| and ||v+w||=||v||+||w||?
一道有关线性代数的题目（题目是用英语出的）For the vectors v=(3,4) and w=(3,4) test the Schwarz inequality on v·w and the triangle inequality on ||v+w||.Find cosA for the angle between v and w.When will we have equality |v·w|=||
1、Schwarz不等式是|v·w|≤||v||×||w||
||v||＝5,||w||＝5,v·w＝25,所以,|v·w|＝25＝||v||×||w||,满足Schwarz不等式.
三角不等式：||v＋w||≤||v||＋||w||
v＋w＝(6,8),||v＋w||＝10,所以||v＋w||＝10＝||v||＋||w||,满足三角不等式.
2、v与w的夹角的余弦cosA＝(v·w)/(||v||×||w||)＝25/(5×5)＝1
3、当且仅当|cosA|＝1,即A＝0或π时,|v·w|＝||v||×||w||
当且仅当cosA＝1,即A＝0时,||v＋w||＝||v||＋||w||