Practicing Success
Practicing Success
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| Which one of the following is not true? |
\(|\vec{a}|=|\vec{b}|\Rightarrow \vec{a}=\vec{b}\) \(|\vec{a}\times \vec{b}|=(\vec{a})^2(\vec{b})^2-(\vec{a}\cdot \vec{b})^2\) \(\vec{a}\times (\vec{b}\cdot \vec{c})\) is not defined If the adjacent sides of a parallelogram are represented by the vectors \(\vec{a}\) and \(\vec{b}\) respectively, then its area is \(|\vec{a}\times \vec{b}|\) |
| \(|\vec{a}|=|\vec{b}|\Rightarrow \vec{a}=\vec{b}\) |
| Counterexample for \(a\): Let \(\vec{a}=\hat{i}+2\hat{j},\vec{b}=\hat{j}-2\hat{k}\) then \(|\vec{a}|=\sqrt{5},|\vec{b}=\sqrt{5}\) but \(\vec{a}\neq \vec{b}\) |
