If the resultant of two forces is equal in magnitude to one of the components and perpendicular to it direction, find the other components using the vector method.

Explanation

Let P be horizontal in the direction of unit vector `hati`. The resultant is also P but perpendicular to it in the direction of unit vector `hatj`. If Q is the other force making an angle `theta`(obtuse) as the resultant is perpendicular to P, then the two forces are `Phati and Q cos theta hati + Q sin theta hatj`. Their resultant is `Phatj`. Therefore,
`" " P hatj = P hati + (Q cos theta hati + Q sin theta hatj)`
Comparing the coefficients of `hati and hatj`, we get
`" " P + Q cos theta = 0 and Q sin theta = P`
or `" "Q cos theta = -P and Q sin theta = P`
Squaring and adding `Q = Psqrt2` and dividing give
`" " tan theta =-1`
`" " theta = 135^(@)`