409 Даны векторы \(\overrightarrow{a}\) {5; -1; 1}, \(\overrightarrow{b}\) {-2; 1; 0}, \(\overrightarrow{c}\) {0; 0,2; 0} и \(\overrightarrow{d}\) {-\(\frac{1}{3}\); 2\(\frac{2}{5}\); -\(\frac{1}{7}\)}. Найдите координаты векторов: а) \(\overrightarrow{a} - \overrightarrow{b}\); б) \(\overrightarrow{b} - \overrightarrow{a}\); в) \(\overrightarrow{a} - \overrightarrow{c}\); г) \(\overrightarrow{d} - \overrightarrow{a}\); д) \(\overrightarrow{c} - \overrightarrow{d}\); е) \(\overrightarrow{a} - \overrightarrow{b} + \overrightarrow{c}\); ж) \(\overrightarrow{a} - \overrightarrow{b} - \overrightarrow{c}\); з) 2\(\overrightarrow{a}\); и) -3\(\overrightarrow{b}\); к) -6\(\overrightarrow{c}\); л) -\(\frac{1}{3}\)\(\overrightarrow{d}\); м) 0,2\(\overrightarrow{b}\).

Ответ: а) {7; -2; 1}, б) {-7; 2; -1}, в) {5; -1,2; 1}, г) {-\(\frac{16}{3}\); 3\(\frac{2}{5}\); -\(\frac{8}{7}\)}, д) {\(\frac{1}{3}\); -2,2; \(\frac{1}{7}\)}, е) {7; -2,2; 1}, ж) {7; -1,8; 1}, з) {10; -2; 2}, и) {6; -3; 0}, к) {0; -1,2; 0}, л) {\(\frac{1}{9}\); -\(\frac{4}{5}\); \(\frac{1}{21}\)}, м) {-0,4; 0,2; 0}

Разбираемся:

а) \(\overrightarrow{a} - \overrightarrow{b}\) = {5-(-2); -1-1; 1-0} = {7; -2; 1}

б) \(\overrightarrow{b} - \overrightarrow{a}\) = {-2-5; 1-(-1); 0-1} = {-7; 2; -1}

в) \(\overrightarrow{a} - \overrightarrow{c}\) = {5-0; -1-0,2; 1-0} = {5; -1,2; 1}

г) \(\overrightarrow{d} - \overrightarrow{a}\) = {-\(\frac{1}{3}\)-5; 2\(\frac{2}{5}\)-(-1); -\(\frac{1}{7}\)-1} = {-\(\frac{16}{3}\); 3\(\frac{2}{5}\); -\(\frac{8}{7}\)}

д) \(\overrightarrow{c} - \overrightarrow{d}\) = {0-(-\(\frac{1}{3}\)); 0,2-2\(\frac{2}{5}\); 0-(-\(\frac{1}{7}\))} = {\(\frac{1}{3}\); -2,2; \(\frac{1}{7}\)}

е) \(\overrightarrow{a} - \overrightarrow{b} + \overrightarrow{c}\) = {5-(-2)+0; -1-1+0,2; 1-0+0} = {7; -1,8; 1}

ж) \(\overrightarrow{a} - \overrightarrow{b} - \overrightarrow{c}\) = {5-(-2)-0; -1-1-0,2; 1-0-0} = {7; -2,2; 1}

з) 2\(\overrightarrow{a}\) = {2⋅5; 2⋅(-1); 2⋅1} = {10; -2; 2}

и) -3\(\overrightarrow{b}\) = {-3⋅(-2); -3⋅1; -3⋅0} = {6; -3; 0}

к) -6\(\overrightarrow{c}\) = {-6⋅0; -6⋅0,2; -6⋅0} = {0; -1,2; 0}

л) -\(\frac{1}{3}\)\(\overrightarrow{d}\) = {- \(\frac{1}{3}\)⋅(-\(\frac{1}{3}\)); -\(\frac{1}{3}\)⋅2\(\frac{2}{5}\); -\(\frac{1}{3}\)⋅(-\(\frac{1}{7}\))} = {\(\frac{1}{9}\); -\(\frac{4}{5}\); \(\frac{1}{21}\)}

м) 0,2\(\overrightarrow{b}\) = {0,2⋅(-2); 0,2⋅1; 0,2⋅0} = {-0,4; 0,2; 0}

Ответ: а) {7; -2; 1}, б) {-7; 2; -1}, в) {5; -1,2; 1}, г) {-\(\frac{16}{3}\); 3\(\frac{2}{5}\); -\(\frac{8}{7}\)}, д) {\(\frac{1}{3}\); -2,2; \(\frac{1}{7}\)}, е) {7; -2,2; 1}, ж) {7; -1,8; 1}, з) {10; -2; 2}, и) {6; -3; 0}, к) {0; -1,2; 0}, л) {\(\frac{1}{9}\); -\(\frac{4}{5}\); \(\frac{1}{21}\)}, м) {-0,4; 0,2; 0}