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Solve the following equation for the vec...

Solve the following equation for the vector `vec p; vec p xx vec a+(vec p. vec b)vec c=vec b xx vec c` where `vec a ,vec b,vec c` are non zero non coplanar vectors and `vec a` is neither perpendicular to `vec b` non to `vec c` hence show that `(vec p xx vec a+([vec a vec b vec c])/(vec a*vec c) vec c)` is perpendicular `vec b-vec c`.

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