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  • the length of the projection of the line segment joining the points {5,-1,4 } and(4,-1,3) on the plane,x+y+z=7 is how to solution its Q

the length of the projection of the line segment joining the points {5,-1,4 } and(4,-1,3) on the plane,x+y+z=7 is how to solution its Q

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best_answer

Vector joining points (5,-1,4) & (4,-1,3) =
                                            \left \{ (5-4)i +(-1-(-1))j+(4-3)k\right \}=i+k
            Vector along normal to the plane=
                                                                  i+j+k
              Unit vector along normal to plane:
                                                                    i/(\sqrt{3})+j/(\sqrt{3})+k/(\sqrt{3})
              So, to find length of projection we do croos product of unit vector along normal of plane & vector joining                    points and then find magnitude of that obtained vector.
                                               \left \{i /(\sqrt{3})+j/(\sqrt{3})+k/(\sqrt{3)} \right \}\ast \left \{ i+k \right \}
                                      =   1/\sqrt{3}(-j)+1/\sqrt{3}(-k)+1/\sqrt{3}(i)+1/\sqrt{3}(j)
                                       
                                    =1/\sqrt{3}(i)+1/\sqrt{3}(-k)
                                         length=\sqrt{2/3} 

Posted by

Rakesh

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