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Two forces act at a point andare such that if the direction of one is reversed, the resultant is turnedthrough a right angle. Show that the two forces must be equal in magnitude. |
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Answer» Let `veca` and `vecb` are the two vectors.Then, their resultant force is `veca+vecb`. If `vecb` is reversed, then their resultant force will be `veca-vecb`. As the resultant turned through aright angle, their dot product should be `0`. `:. (veca+vecb)(veca-vecb) = 0` `=>vec.veca+veca.vecb-vecb.veca-vecb.vecb = 0` `=>vec.veca - veb.vecb = 0` `=>|a|^2 - |b|^2 = 0` `=> |a|^2 = |b|^2` `=> |a| = |b|` `:.` Magnitude of these two vectors are equal. |
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