Вектор АВ= (5-1=4; 2-(-2)=4; -3-2=-5) = (4; 4; -5). |AB| = √(16+16+25) = √57.
Вектор АС= (5-1=4; -1-(-2)=1; 4-2=2) = (4; 1; 2). |AC| = √(16+1+4) = √21.
Скалярное произведение АВхАС = 16+4-10 = 10.
cos(BAC) = 10/(√57*√21) = 10/√1197 = 10/(3√133) ≈ 0,289037.
∠BAC = arc cos 0,289037 = 1,2776 радиан = 73,2 градуса.
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Вектор АВ= (5-1=4; 2-(-2)=4; -3-2=-5) = (4; 4; -5). |AB| = √(16+16+25) = √57.
Вектор АС= (5-1=4; -1-(-2)=1; 4-2=2) = (4; 1; 2). |AC| = √(16+1+4) = √21.
Скалярное произведение АВхАС = 16+4-10 = 10.
cos(BAC) = 10/(√57*√21) = 10/√1197 = 10/(3√133) ≈ 0,289037.
∠BAC = arc cos 0,289037 = 1,2776 радиан = 73,2 градуса.