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.
Solution:
Let $\Theta$ be the angle between them.
Then, using the relation $\mathrm{R}^{2}=\mathrm{A}^{2}+\mathrm{B}^{2}+2 \mathrm{AB} \cos \theta$,
a)
We get for $R=1$,
$1=9+16+24 \operatorname{Cos} \theta$
Or, $\theta=180^{\circ}$
b)
For, $R=5$, we have
$25=9+16+24 \operatorname{Cos} \theta$
Or, $\cos \theta=0$
$\theta=90^{\circ}$
c)For $R=7$
$49=9+16+24 \operatorname{Cos} \theta$
Or $\cos \theta=1$,
And $\theta=0^{\circ}$
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