First slide

Vectors

Question

$Two forces \vec{P} and \vec{Q} have a resultant perpendicular to \vec{P} . The angle between the forces is$

Moderate

A

$\tan^{- 1} (\frac{- P}{Q})$
B

$c {os}^{- 1} (\frac{P}{Q})$
C

$s {in}^{- 1} (\frac{P}{Q})$
D

$\cos^{- 1} (\frac{- P}{Q})$

Solution

$\tan α = \frac{Qsin θ}{P + Qcos θ} where α = angle made by \vec{R} with \vec{P} and θ = angle between \vec{P} and \vec{Q} Here, α = 90^{\circ}, \tan α = \tan 90^{\circ} = \infty \begin{array}{l} ∴ P + Qcos θ = 0 \\ \Rightarrow \cos θ = \frac{- P}{Q} \\ \Rightarrow θ = \cos^{- 1} (\frac{- P}{Q}) \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App