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Question

In a two dimensional motion, a particle moves from point A (position vector r1), to point B (position vector r2). If the magnitudes of these vectors are r1=3 m and r2=4 m and the angles they make with the x-axis are θ1=75 and θ2=15, respectively, then the magnitude of the displacement vector (in m) is

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Solution

Displacement = AB, angle between r1 and r2:θ=7515=60

AB2=r21+r222r1r2 cos θ
=32+422×3×4 cos 60=13
AB=13 m

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