MCQ
If the sum of two unit vectors is also a unit vector. then magnitude of their difference and angle between the two given unit vectors is ..............
  • A
    $\sqrt{3}, 60^{\circ}$
  • $\sqrt{3}, 120^{\circ}$
  • C
    $\sqrt{2}, 60^{\circ}$
  • D
    $\sqrt{2}, 120^{\circ}$

Answer

Correct option: B.
$\sqrt{3}, 120^{\circ}$
b
(b)

$|\vec{R}|=|\vec{A}+\vec{B}|=\sqrt{A^2+B^2+2 A B \cos \theta}$

$|\vec{A}|=|\vec{B}|=|\vec{R}|=1$

$1=1+1+2 \times 1 \times 1 \times \cos \theta$

$\cos \theta=-\frac{1}{2} \Rightarrow \theta=120^{\circ}$

$|\vec{R}|=|\vec{A}-\vec{B}|=\sqrt{A^2+B^2-2 A B \cos 120^{\circ}}$

$=\sqrt{1^2+1^2-2 \times 1 \times 1 \times\left(-\frac{1}{2}\right)}=\sqrt{3}=|\vec{A}-\vec{B}|$

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