Solve the following

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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