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stuart clark

stuart clark

Đăng ký: 23-02-2011
Offline Đăng nhập: 22-02-2023 - 21:45
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Trong chủ đề: Tim Max $(3\sqrt{2}y-\sqrt{11}z)^2+(...

09-05-2019 - 22:10

Let $\displaystyle \vec{a} = x\hat{i}+y\hat{j}+z\hat{k}$ and $\displaystyle \vec{b} = \sqrt{7}\hat{i}+\sqrt{11}\hat{j}+3\sqrt{2}\hat{k}$
 
Using $\bigg|\vec{a}\times \vec{b}\bigg|^2=|\vec{a}|^2|\vec{b}|^2-\bigg(\vec{a}\cdot \vec{b}\bigg)\leq |\vec{a}|^2|\vec{b}|^2$
 
So 
 
$(3\sqrt{2}y-\sqrt{11}z)^2+(\sqrt{7}z-3\sqrt{2}x)^2+(\sqrt{11}x-\sqrt{7}y)^2\leq 36$
 
Equality hold when $\sqrt{7}x+\sqrt{11}y+3\sqrt{z}=0.$