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JEE Main 2024 (4 Apr, Shift 1) · Addition & Subtraction of Vectors

Addition & Subtraction of Vectors question from JEE Main 2024 (4 Apr, Shift 1)

Q13JEE Main 2024 · 4 APR · SHIFT 1Medium

Addition & Subtraction of Vectors

Two forces $\overline{F}_1$ and $\overline{F}_2$ are acting on a body. One force has magnitude thrice that of the other force and the resultant of the two forces is equal to the force of larger magnitude. The angle between $\vec{F}_1$ and $\vec{F}_2$ is $\cos^{-1}\left(\frac{1}{n}\right)$ . The value of $|n|$ is _______.

Numerical answer type. Work it out, then open the answer.

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Answer: 6

Let the forces be $F$ and $3F$ , resultant $R = 3F$ .
$9F^2 = F^2 + 9F^2 + 6F^2\cos\theta \Rightarrow \cos\theta = -\frac{1}{6}$
So $\theta = \cos^{-1}\left(-\frac{1}{6}\right)$ , i.e. $n = -6$ .
Answer: $|n| = 6$

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