91影视

The indicated quantities when $u=(鈭�3,1,鈭�4),v=(2,0,5),\mathrm{and}w=(1,3,13)$

We have to find the value of$(u脳v)路w\mathrm{and}u路(v脳w)$

To just take the absolute value of the determinant of the 3 脳 3 matrix formed from the components of u, v and w as the rows.

The required cross product of $(u脳v)路w$

$(u脳v)路w=\det \left[\begin{array}{ccc}-3& 1& -4\\ 2& 0& 5\\ 1& 3& 13\end{array}\right]$

$$\begin{gathered} (u脳v)路w=\det \left[\begin{array}{ccc}-3& 1& -4\\ 2& 0& 5\\ 1& 3& 13\end{array}\right] \\ (u脳v)路w=-3\left|\begin{array}{cc}0& 5\\ 3& 13\end{array}\right|-1\left|\begin{array}{cc}2& 5\\ 1& 13\end{array}\right|-4\left|\begin{array}{cc}2& 0\\ 1& 3\end{array}\right| \\ (u脳v)路w=-3(0脳13-5脳3)-1(2脳13-5脳1)-4(2脳3-0脳1) \\ (u脳v)路w=-3(0-15)-1(26-5)-4(6-0) \\ (u脳v)路w=45-21-24 \\ (u脳v)路w=0 \end{gathered}$$

To just take the absolute value of the determinant of the 3 脳 3 matrix formed from the components of u, v and w as the rows.

The required cross product of $u路(v脳w)$

$u路(v脳w)=\det \left[\begin{array}{ccc}-3& 1& -4\\ 2& 0& 5\\ 1& 3& 13\end{array}\right]$

$$\begin{gathered} u路(v脳w)=\det \left[\begin{array}{ccc}-3& 1& -4\\ 2& 0& 5\\ 1& 3& 13\end{array}\right] \\ u路(v脳w)=-3\left|\begin{array}{cc}0& 5\\ 3& 13\end{array}\right|-1\left|\begin{array}{cc}2& 5\\ 1& 13\end{array}\right|-4\left|\begin{array}{cc}2& 0\\ 1& 3\end{array}\right| \\ u路(v脳w)=-3(0脳13-5脳3)-1(2脳13-5脳1)-4(2脳3-0脳1) \\ u路(v脳w)=-3(0-15)-1(26-5)-4(6-0) \\ u路(v脳w)=45-21-24 \\ u路(v脳w)=0 \end{gathered}$$