Question

Determinar o vetor v colinear ao vetor u = ( -4, 2, 6), tal que v.w = 12 sendo w = ( -1, 4, 2)

Answer 1

Olá, Ygor.

$\text{Se }v\text{ \'e colinear a }u\text{, ent\~ao }v = \alpha(-4,2,6),\alpha\in\mathbb{R}.\\\\ \text{Como }v\cdot w = 12,\text{ temos que }\alpha(-4,2,6)\cdot(-1,4,2)=12\Rightarrow\\\\ \alpha[(-4)(-1)+2\cdot4+6\cdot2]=12 \Rightarrow \alpha[4+8+12]=12 \Rightarrow\\\\ \alpha\cdot24=12 \Rightarrow \alpha=\frac12$

Portanto, $v=\frac12\cdot(-4,2,6) \Rightarrow\boxed{v=(-2,1,3)}$