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the resultant of two forces acting at an angle of $150{}^\circ$is $10N$ and its perpendicular to one of the forces. The two others force is:
(A) $\dfrac{20}{\sqrt{3}}N$
(B) $\dfrac{10}{\sqrt{3}}N$
(C) 20N
(D) $\dfrac{20}{3}N\,$

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Last updated date: 20th Jun 2024
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Answer
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Hint: In physics, a vector is a quantity that has both magnitude and direction. It is typically represented by an arrow whose direction is the same as that of the quantity and whose length is proportional to the given quantity’s magnitude. Although a vector consists of magnitude and direction, it does not consist of a position. With this information in mind, we can easily solve such types of questions.

Complete step-by step answer:
Let the two forces mentioned in the above questions be A and B.
Let R be the resultant force of the force vectors A and B.
R is perpendicular in direction to the B vector.
We can determine from the given information that, $A\cos (60{}^\circ )=R=10\Rightarrow A=20N$
$\Rightarrow A\sin (60{}^\circ )=B\Rightarrow 10\sqrt{3}N$
$\therefore$Forces are 20N and $10\sqrt{3} N$.

Hence, the correct answer is Option C.

Note: We must keep in mind the various properties of a vector to be able to equate the given question. We must know how two vectors act when in parallel or perpendicular to each other.