CDF POINTS
1. If \( \overrightarrow P \text{ }and\text{ }\overrightarrow Q \) are two vectors their resultant vector is given by \( \overrightarrow R = \overrightarrow P + \overrightarrow Q \).
2. The magnitude of resultant \(\overrightarrow R\) is \( R = \sqrt {P^2 + Q^2 + 2PQ\cos \theta } \)
3. If \(\overrightarrow R\) makes an angle \(\alpha\) with \(\overrightarrow P\), then \( \tan \alpha = \frac{{Q\sin \theta }} {{P + Q\cos \theta }} \)
4. If \(\overrightarrow R\) makes an angle \(\beta\) with \(\overrightarrow Q\) then \(
\tan \beta = \frac{{P\sin \theta }}
{{Q + P\cos \theta }}
\)
5. Resultant of two vectors always lies in the plane containing the vectors closer to vector of larger magnitude.
6. Special cases
i) \(
\theta = 0^0 \Rightarrow R\left( {\max } \right) = P + Q
\)
ii) \(
\theta = 180^0 \Rightarrow R\left( {\min } \right) = P - Q
\)
iii) \(
\theta = 90^0 \Rightarrow R = \sqrt {P^2 + Q^2 }
\) and \(
\tan \alpha = \frac{Q}
{P}
\)
iv) \(
P = Q \Rightarrow R = 2P\cos \left( {\frac{\theta }
{2}} \right)\& \alpha = \frac{\theta }
{2}
\)