Two forces act at a point and are such that if the direction of one is reversed, the resultant is turned through a right angle. Show that the two forces must be equal in magnitude.

Explanation

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`

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