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:
  1. 1 unit.
  2. 5 unit.
  3. 7 unit.

Answer

$|\vec{\text{a}}|=3\text{m},|\vec{\text{b}}|=4$
  1. If R = 1 unit
$\Rightarrow\sqrt{3^2+4^2+2.3.4.\cos\theta}=1$
$\Rightarrow\theta=180^{\circ}$
  1. $\sqrt{3^2+4^2+2.3.4\cos\theta}=5$
$\Rightarrow\theta=90^{\circ}$
  1. $\sqrt{3^2+4^2+2.3.4\cos\theta}=7$
$\Rightarrow\theta=0^{\circ}$
Angle between them is 0°.

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