First slide

Vectors

Question

The resultant of two forces, one double of the other magnitude, is perpendicular to the smaller of two forces. The angle between the two force is

Easy

A

60°
B

120°
C

150°
D

90°

Solution

See figure. P and Q (2P) are two forces and their resultant is R. The angle between P and Q is $α$ .
From figure, $\cos θ = \frac{P}{Q} = \frac{P}{2 P} = \frac{1}{2}$
$\begin{array}{ll} ∴ θ = \cos^{- 1} (\frac{1}{2}) = 60^{\circ} \\ So, α = 180^{\circ} - 60^{\circ} = 120^{\circ} \end{array}$

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