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

Ответ: а) {3; 2; 1}, б) {3 \(\frac{2}{3}\); -5; 2}, в) {\(\frac{2}{3}\); 7; -1}, г) {-2,7; 10,1; -0,5}, д) {0,3; -1,9; 2,5}, е) {3 \(\frac{2}{3}\); 2; 1}, ж) {0,3; 6; -1,5}, з) {0,3; 1,9; 1,5}

Разбираемся:

а) \(\overrightarrow{a} + \overrightarrow{b}\) = {3+0; -5+7; 2+(-1)} = {3; 2; 1}

б) \(\overrightarrow{a} + \overrightarrow{c}\) = {3+\(\frac{2}{3}\); -5+0; 2+0} = {3\(\frac{2}{3}\); -5; 2}

в) \(\overrightarrow{b} + \overrightarrow{c}\) = {0+\(\frac{2}{3}\); 7+0; -1+0} = {\(\frac{2}{3}\); 7; -1}

г) \(\overrightarrow{d} + \overrightarrow{b}\) = {-2,7+0; 3,1+7; 0,5+(-1)} = {-2,7; 10,1; -0,5}

д) \(\overrightarrow{d} + \overrightarrow{a}\) = {-2,7+3; 3,1+(-5); 0,5+2} = {0,3; -1,9; 2,5}

е) \(\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c}\) = {3+0+\(\frac{2}{3}\); -5+7+0; 2+(-1)+0} = {3\(\frac{2}{3}\); 2; 1}

ж) \(\overrightarrow{b} + \overrightarrow{a} + \overrightarrow{d}\) = {0+3+(-2,7); 7+(-5)+3,1; -1+2+0,5} = {0,3; 5,1; 1,5}

з) \(\overrightarrow{a} + \overrightarrow{b} + \overrightarrow{c} + \overrightarrow{d}\) = {3+0+\(\frac{2}{3}\)+(-2,7); -5+7+0+3,1; 2+(-1)+0+0,5} = {0,3; 5,1; 1,5}

Ответ: а) {3; 2; 1}, б) {3 \(\frac{2}{3}\); -5; 2}, в) {\(\frac{2}{3}\); 7; -1}, г) {-2,7; 10,1; -0,5}, д) {0,3; -1,9; 2,5}, е) {3 \(\frac{2}{3}\); 2; 1}, ж) {0,3; 6; -1,5}, з) {0,3; 1,9; 1,5}