Calculate the angle between the two vectors of magnitude 4n and 3N if their resultant is 6.083 n

Text Solution

Answer : 1N

Solution : `theta=180^(@)`, both the forces are antiparallel, `R=A-B` <br> `therefore` Net force or resultant force `R=4-3=1N` <br> Direction of net force is along bigger force means along 4N. <br> <img src="https://d10lpgp6xz60nq.cloudfront.net/physics_images/VMC_NEET_XI_PHY_MOD_00_C01_SLV_059_S01.png" width="80%">

Feel free to ask doubts in the Comment Section.

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Good Luck!

Hello!

We can assume the two forces to be f1 and 2 Therefore, f1²+f2²=10 Since the angle between them is 90 degrees when angle is 60 f1²+f2²+2*f1*f2*cos(60)=13 10+f1*f2=13 3=f1*f2 (f1+f2)²=f1²+f2²+2*f1*f2=10+6=16 f1+f2=4........................................(1) f1-f2=√((f1+f2)²-4f1*f2)=2...........(2)

Therefore,

from (1) and (2) u get
f1= 3 N

f2= 1 N

Hope this helps you!

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Given two forces, the largest magnitude their sum (resultant) can have is the sum of their magnitudes (this occurs when they point in the same direction) while the smallest magnitude their sum can have is the difference of their magnitudes (when they point in opposite directions).

Therefore, in your example, the largest possible resultant magnitude is $6\,\mathrm N + 4 \,\mathrm N = 10 \,\mathrm N$. None of the answer choices violates this upper bound.

Now think about whether one of the choices violates the lower bound described above.