Ответы
Ответ дал:
0
Решаем через смешанное произведение векторов
![vec{a}cdotvec{b} = x_acdot x_b + y_acdot y_b = |vec{a}|cdot|vec{b}|cdot cos(alpha)\
cos(alpha) = frac{(x_acdot x_b + y_acdot y_b)}{|vec{a}|cdot|vec{b}|}\
cos(alpha) = frac{(-1cdot 3 + 2cdot 1)}{ sqrt{ (-1)^{2}+2^{2}} cdot sqrt{ 3^{2}+1^{2}}} = frac{-1}{ sqrt{5} cdot sqrt{ 10 }} = frac{-1}{ 5cdotsqrt{2} }\
alpha = arccos(frac{-1}{ 5cdotsqrt{2} }) approx 98,13 ^{circ}](https://tex.z-dn.net/?f=vec%7Ba%7Dcdotvec%7Bb%7D+%3D+++x_acdot+x_b+%2B+y_acdot+y_b+%3D+%7Cvec%7Ba%7D%7Ccdot%7Cvec%7Bb%7D%7Ccdot+cos%28alpha%29%5C%0Acos%28alpha%29+%3D+frac%7B%28x_acdot+x_b+%2B+y_acdot+y_b%29%7D%7B%7Cvec%7Ba%7D%7Ccdot%7Cvec%7Bb%7D%7C%7D%5C%0Acos%28alpha%29+%3D+frac%7B%28-1cdot+3+%2B+2cdot+1%29%7D%7B+sqrt%7B+%28-1%29%5E%7B2%7D%2B2%5E%7B2%7D%7D+cdot+sqrt%7B+3%5E%7B2%7D%2B1%5E%7B2%7D%7D%7D+%3D+frac%7B-1%7D%7B+sqrt%7B5%7D+cdot+sqrt%7B+10+%7D%7D+%3D+frac%7B-1%7D%7B+5cdotsqrt%7B2%7D+%7D%5C%0Aalpha+%3D+arccos%28frac%7B-1%7D%7B+5cdotsqrt%7B2%7D+%7D%29+approx+98%2C13+%5E%7Bcirc%7D%0A%0A "vec{a}cdotvec{b} = x_acdot x_b + y_acdot y_b = |vec{a}|cdot|vec{b}|cdot cos(alpha)\
cos(alpha) = frac{(x_acdot x_b + y_acdot y_b)}{|vec{a}|cdot|vec{b}|}\
cos(alpha) = frac{(-1cdot 3 + 2cdot 1)}{ sqrt{ (-1)^{2}+2^{2}} cdot sqrt{ 3^{2}+1^{2}}} = frac{-1}{ sqrt{5} cdot sqrt{ 10 }} = frac{-1}{ 5cdotsqrt{2} }\
alpha = arccos(frac{-1}{ 5cdotsqrt{2} }) approx 98,13 ^{circ}")
Приложения:
Похожие вопросы
2 года назад
2 года назад
2 года назад
8 лет назад
9 лет назад