Question

Найдите угол между векторами а(7;0;-1) и b(7;4;4)

Answer 1

$\cos(\widehat{a,b})= \frac{ab}{|a|\,\,|b|} \\ ab=x_ax_b+y_ay_b+z_az_b=45 \\ |a|= \sqrt{49+1} \approx7.07 \\ |b|= \sqrt{7^2+4^2+4^2}=9 \\ \\ \cos(\widehat{a,b})= \frac{45}{7.07\cdot9}\approx0.7071\\ \\ \widehat{a,b}=\arccos(0.7071)=45а$