Assume that (vector u) dot product ((vector v) cross product (vector w)) = 20 then compute  (b) (vector v) dot product (2(vector u) cross product 4(vector w))

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rakesh05 | High School Teacher | (Level 1) Assistant Educator

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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)`

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

Now we have to find  `v.(2uxx4w)=8{v.(uxxw)}`   (as we can take scalars out)

                                                   `=8det[[v_1,v_2,v_3],[u_1,u_2,u_3],[w_1,w_2,w_3]]`

                                                 `=8(-1)det[[u_1,u_2,u_3],[v_1,v_2,v_3],[w_1,w_2,w_3]]`

                                                `=8(-1)20=-160.`

As by the rule if we interchange any two rows, the result is multiplied by (-1).

                                             

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