Assume that (vector u) dot product ((vector v) cross product (vector w)) = 20 then compute     (c) (vector u) dot product ((vector u) cross product (vector w))

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Let  `u=(u_1,u_2,u_3),v=(v_1,v_2,v_3),w=(w_1,w_2,w_3)` .

Now   `u.(vxxw)=det[[u_1,u_2,u_3],[v_1,v_2,v_3],[w_1,w_2,w_3]]` .

By given problem, `u.(vxxw)=20` .

We want to find `u.(uxxw)` .

Now,     `u.(uxxw)=det[[u_1,u_2,u_3],[u_1,u_2,u_3],[w_1,w_2,w_3]]` .

By the rule of determinant, if any two rows are same then the value of the determinant is zero. In the above we see that first and the second rows...

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Let  `u=(u_1,u_2,u_3),v=(v_1,v_2,v_3),w=(w_1,w_2,w_3)` .

Now   `u.(vxxw)=det[[u_1,u_2,u_3],[v_1,v_2,v_3],[w_1,w_2,w_3]]` .

By given problem, `u.(vxxw)=20` .

We want to find `u.(uxxw)` .

Now,     `u.(uxxw)=det[[u_1,u_2,u_3],[u_1,u_2,u_3],[w_1,w_2,w_3]]` .

By the rule of determinant, if any two rows are same then the value of the determinant is zero. In the above we see that first and the second rows are the same.

So,     `u.(uxxw)=0` . Answer.

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