Question

two vectors of equal magnitude P are inclined at some angle such that the difference in the magnitude of resultant and magnitude of either of the vectors is 0.732 X either of the magnitude of vector if the angle between them is increased by the half of its initial value then find the magnitude of difference of two vectors

Answer 1

Let each vector has a magnitude a which makes an angle θ between them hence the resultant (R) of these equal vectors

R=a2+a2+2a⋅acosθ−−−−−−−−−−−−−−−−√

=2a2+2a2cosθ−−−−−−−−−−−−√

=a2–√1+cosθ−−−−−−−√

=a2–√1+2cos2θ2−1−−−−−−−−−−−−−√

=a2–√2cos2θ2−−−−−−√

=a2–√2–√cosθ2

=2acosθ2

& the resultant will be equally inclined at an angle θ2 with the equal vectors or the resultant acts along the angle bisector of both the equal vectors