3-36 할리데이 10판 솔루션 일반물리학

$$\begin{cases} \vec p_1 = 4\hat i - 3 \hat j\\ \vec p_2= -6\hat i + 3\hat j - 2\hat k\\ \end{cases} $$ $$ \begin{aligned} \Ans =& (\vec p_1 + \vec p_2)\cdot(\vec p_1\times \vec p_2)\\ =&\bra{(-2)\i+(-2)\k}\cdot \begin{vmatrix} \i & \j & \k\\ 4&-3&0\\ -6&3&-2\\ \end{vmatrix}\\ =&\bra{(-2)\i+(-2)\k}\\ &\cdot\( \begin{vmatrix} -3&0\\ 3&-2\\ \end{vmatrix}\i+ \begin{vmatrix} 0&4\\ -2&-6\\ \end{vmatrix}\j+ \begin{vmatrix} -3&0\\ 3&-2\\ \end{vmatrix}\k\)\\ =&\bra{(-2)\i+(-2)\k}\cdot\bra{6\i+8\j+(-6)\k}\\ =&0 \end{aligned} $$