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(A) According to the triangle inequality for vectors,for any two vectors $\vec{a}$ and $\vec{b}$,the magnitude of their sum is always less than or equ

Vedclass · Accepted Answer

$|\vec{a} + \vec{b}| \ge |\vec{a}| - |\vec{b}|$

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(A) According to the triangle inequality for vectors,for any two vectors $\vec{a}$ and $\vec{b}$,the magnitude of their sum is always less than or equal to the sum of their magnitudes,i.e.,$|\vec{a} + \vec{b}| \le |\vec{a}| + |\vec{b}|$.Also,the reverse triangle inequality states that $|\vec{a} + \vec{b}| \ge ||\vec{a}| - |\vec{b}||$.Since $|\vec{a}| - |\vec{b}| \le ||\vec{a}| - |\vec{b}||$,it follows that $|\vec{a} + \vec{b}| \ge |\vec{a}| - |\vec{b}|$.Therefore,the statement $|\vec{a} + \vec{b}| \ge |\vec{a}| - |\vec{b}|$ is always true.

For any two vectors $\vec{a}$ and $\vec{b}$,which of the following statements is true?

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