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Question

In a two - dimensional motion of a particle, the particle moves from point A, with position vector [r1], to point B, with position vector r2. If the magnitudes of these vectors are , respectively, r1=3 and r2=4 and the angles they make with the x - axis are θ1=75o and θ2=15o respectively, then find the magnitude of the displacement vector.
1107866_795f994808fc4d3995ea792535d8c9b5.png

A
15
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B
13
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C
17
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D
15
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Solution

The correct option is B 13

Given that,

r1=3

r2=4

θ1=750

θ2=150

By cosine rule

z2=r21+r222r1r2cos(θ1θ2)

z2=(3)2+(4)22×3×4cos600

z2=9+1612

z=13

Hence, the magnitude of the displacement vector is 13


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