Question

If the sum of two vectors is a unit vector, then the magnitude of their difference is

• A. $\sqrt{2}$
• B. $\sqrt{3}$
• C. $\frac{1}{\sqrt{3}}$
• D. 1

Answer 1

Answer: (B)

$\sqrt{3}$

Answer 2

Let $|\mathbf{a}| = 1$, $|\mathbf{b}| = 1$ and $|\mathbf{a} + \mathbf{b}| = 1$ ⇒ $|\mathbf{a} + \mathbf{b}|^{2} = 1$

⇒$1 + 1 + 2\cos\theta = 1$ ⇒ $\cos\theta = - \frac{1}{2}$ ⇒ $\theta = 120^{o}$

$\mathbf{\therefore}$ $\mathbf{|a - b}\mathbf{|}^{\mathbf{2}}\mathbf{= 1 + 1 - 2}\mathbf{\cos}\mathbf{\theta}\mathbf{= 3}$ ⇒ $|\mathbf{a} - \mathbf{b}| = \sqrt{3}$