Question

Khẳng định nào sau đây là đúng?

\( A. \exists \; \overrightarrow{a},\; \left|\overrightarrow{a}\right|^{2} \ne \left|\overrightarrow{a}^{2} \right|.\) \(B. \forall \; \overrightarrow{a},\; \left|\overrightarrow{a}\right|^{2} =\left|\overrightarrow{a}^{2} \right|.\)

\(C. \forall \; \overrightarrow{a},\; \left|\overrightarrow{a}\right|^{2} \ne \left|\overrightarrow{a}^{2} \right|.\)  \(D. \forall \; \overrightarrow{a},\; \left|\overrightarrow{a}\right|^{2} >0.\)
 

Answer 1

Chọn B

 Ta có: \(\overrightarrow{a}.\overrightarrow{a}=\left|\overrightarrow{a}\right|.\left|\overrightarrow{a}\right|.co{\rm s}\left(\overrightarrow{a},\overrightarrow{a}\right).\) Mà\( \forall \overrightarrow{a} \)

Ta có: \(\overrightarrow{a}.\overrightarrow{a}=\left|\overrightarrow{a}^{2} \right|nên\left|\overrightarrow{a}\right|^{2} =\left|\overrightarrow{a}\right|^{2} .co{\rm s0}. \Rightarrow \; \; \left|\overrightarrow{a}\right|^{2} =\left|\overrightarrow{a}^{2} \right|.\)