3-38 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec A = 2.00\i + 3.00\j - 4.00\k\\ \vec B = -3.00\i + 4.00\j+ 2 .00\k\\ \vec C= 7.00\i- 8.00 \j\\ \end{cases} $$ $$3\vec C\cdot (2\vec A \times \vec B)=?$$ $$ \begin{aligned} \Ans=&3\vec C\cdot (2\vec A \times \vec B)\\ =&3\vec C\cdot \begin{vmatrix} \i & \j & \k\\ 4 &6 &-8 \\ -3 &4 &2 \\ \end{vmatrix}\\ =&3\vec C\cdot \( \begin{vmatrix} 6 &-8 \\ 4 &2 \\ \end{vmatrix}\i+ \begin{vmatrix} -8&4 \\ 2&-3 \\ \end{vmatrix}\j+ \begin{vmatrix} 4 &6 \\ -3 &4 \\ \end{vmatrix}\k \)\\ =&3(7.00\i- 8.00 \j)\cdot(44\i+16\j+34\k)\\ =&1308 \end{aligned} $$