Question

помогите срочно!!!!!​

Answer 1

Ответ:

$| \overrightarrow{a} - \overrightarrow{b}| = \sqrt{19}$

$\sqrt{(\overrightarrow{a} - \overrightarrow{b})^{2} } = \sqrt{19}$

$\sqrt{ {\overrightarrow{a}}^{2} - 2\overrightarrow{a}\overrightarrow{b} + {\overrightarrow{b}}^{2} } = \sqrt{19}$

Возведем обе части в квадрат

$\overrightarrow{a}^{2} - 2\overrightarrow{a}\overrightarrow{b} + {\overrightarrow{b}}^{2} = 19$

Если что: ${\overrightarrow{a}}^{2}= |{\overrightarrow{a}}|^{2}$

${3}^{2} - 2\overrightarrow{a}\overrightarrow{b} + {5}^{2} = 19 \\ 9 - 2\overrightarrow{a}\overrightarrow{b} + 25 = 19 \\ 34 - 2\overrightarrow{a}\overrightarrow{b} = 19 \\ - 2\overrightarrow{a}\overrightarrow{b} = 19 - 34 \\ - 2\overrightarrow{a}\overrightarrow{b} = - 15 \\ 2\overrightarrow{a}\overrightarrow{b} = 15$

$|\overrightarrow{a} + \overrightarrow{b}| = \sqrt{( {\overrightarrow{a} + \overrightarrow{b})}^{2} } = \sqrt{ {\overrightarrow{a}}^{2} + 2\overrightarrow{a}\overrightarrow{b} +{\overrightarrow{b}}^{2} }$

$\sqrt{ {3}^{2} + 15 + {5}^{2} } = \sqrt{9 + 15 + 25} = \sqrt{49} = 7$

Ответ:

$|\overrightarrow{a} + \overrightarrow{b}| = 7$