The sum of two forces P and Q is R such that |R| = |P|. The angle θ (in degrees) that the resultant of 2 P and Q will make with Q is.............. Numerical answer type. Work it out, then open the answer.

Answer: 90. |P + Q|² = P² ⇒ Q² + 2P · Q = 0. (2P + Q) · Q = 2P · Q + Q² = 0 Zero dot product means (2P + Q) ⊥ Q. Answer: θ = 90°

The sum of two forces P and Q is R such that |R| = |P|. The angle θ… | JEE Main 2020 (7 Jan, Shift 2)

Q26JEE Main 2020 · 7 JAN · SHIFT 2Difficult

Addition & Subtraction of Vectors

The sum of two forces $\vec{P}$ and $\vec{Q}$ is $\vec{R}$ such that $\left|\vec{R}\right| = \left|\vec{P}\right|$ . The angle $\theta$ (in degrees) that the resultant of 2 $\vec{P}$ and $\vec{Q}$ will make with $\vec{Q}$ is ..............

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

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Answer: 90

$|\vec{P} + \vec{Q}|^2 = P^2 \Rightarrow Q^2 + 2\vec{P} \cdot \vec{Q} = 0$ .
$(2\vec{P} + \vec{Q}) \cdot \vec{Q} = 2\vec{P} \cdot \vec{Q} + Q^2 = 0$
Zero dot product means $(2\vec{P} + \vec{Q}) \perp \vec{Q}$ .
Answer: $\theta = 90^\circ$

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Addition & Subtraction of Vectors question from JEE Main 2020 (7 Jan, Shift 2)

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