First slide

Scalars and Vectors

Question

If the resultant of two forces of magnitude p and 2p is perpendicular to p, then the angle between the forces is

Moderate

A

$\frac{2 π}{3}$
B

$\frac{3 π}{4}$
C

$\frac{4 π}{5}$
D

$\frac{5 π}{6}$

Solution

$\begin{array}{l} \tan α = \frac{2 p \sin θ}{p + 2 p \cos θ} here θ = 90^{\circ} \\ \Rightarrow \infty = \frac{2 p \sin θ}{p + 2 p \cos θ} \Rightarrow p + 2 p \cos θ = 0 \\ \Rightarrow \cos θ = \frac{1}{2} \Rightarrow θ = \frac{2 π}{3} \end{array}$

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