Question

Two vectors have magnitudes 3 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.

Answer 1

$|\overrightarrow{a}|=3,|\overrightarrow{b}|=4$,
(a) If R = 1 unit, then
$\sqrt{3^2+4^2+\mathrm{2.3.4}cos\theta =1}$
\Rightarrow 25+24 ~cos~ \theta= 1 \\
\Rightarrow 24 ~ cos~\theta =- 24\\
\Rightarrow cos~\theta =- 1\\
\Rightarrow \theta =180^0\)

(b) $\sqrt{3^2+4^2+\mathrm{2.3.4}cos\theta =5}\Rightarrow 25+24cos\theta =25\Rightarrow 24cos\theta =0\Rightarrow cos\theta ={90}^0$

(c) $\sqrt{3^2+4^2+\mathrm{2.3.4}cos\theta =7}\Rightarrow 25+24cos\theta =49,\Rightarrow 24cos\theta =24\Rightarrow cos\theta =1\Rightarrow \theta =co{s}^{-1}1=0^0$

Hence angle between them is $0^0$