Respuestas
El valor de la operación entre vectores es:
a ⋅ (b × c) + 2a ⋅ c - b ⋅ a = 21
Los vectores en cuestión son:
- a = (−2;−2;−1)= -2i-2j-k;
- b = 2j−3i+2k = (2; -3; 2);
- c = −i+2j+4k = (-1; 2; 4);
Determine: a⋅(b × c)+2a⋅c−b⋅a
Producto vectorial;
(b × c) = i j k
2 -3 2
-1 2 4
(b × c) = i[(-3)(4)-(2)(2)] -j[(2)(4)-(-1)(2)]+k[(2)(2)-(-1)(-3)]
(b × c) = (-16i + 10j + k)
Producto punto;
a⋅(b × c) = (−2;−2;−1)(-16; 10; 1)
a⋅(b × c) = (-2)(-16) + (-2)(10) + (-1)(1)
a⋅(b × c) = 32-20-1
a⋅(b × c) = 11
2a ⋅ c = 2(−2;−2;−1)(-1; 2; 4)
2a ⋅ c = (-4; -4; -2)(-1; 2; 4)
2a ⋅ c = (-4)(-1) + (-4)(2) + (-2)(4)
2a ⋅ c = 4 - 8 - 8
2a ⋅ c = -12
b ⋅ a = (2; -3; 2)(−2;−2;−1)
b ⋅ a = (2)(-2) + (-3)(-2) + (2)(-1)
b ⋅ a = -4 + 6 - 24
b ⋅ a = -22
Sustituir;
a ⋅ (b × c) + 2a ⋅ c - b ⋅ a = 11 + (-12) - (-22)
a ⋅ (b × c) + 2a ⋅ c - b ⋅ a = 21