Question

If a and b are adjacent sides of a rhombus, then

• A. a.b = 0
• B. a × b = 0
• C. a.a = b.b
• D. None of these

Answer 1

Answer: (C)

a.a = b.b

Answer 2

$\because$ $\mathbf{a}.\mathbf{a} = |\mathbf{a}||\mathbf{a}|\cos\theta = |\mathbf{a}|^{2}$, $(\because\theta = 0^{o})$

and $\mathbf{b}.\mathbf{b} = |\mathbf{b}||\mathbf{b}|\cos\theta = |\mathbf{b}|^{2}$, (Here$\theta = 0^{o}$)

Also, since $\mathbf{a}\text{and}\mathbf{b}$ are sides of rhombus

∴ $|\mathbf{a}| = |\mathbf{b}|$. Hence $\mathbf{a}.\mathbf{a} = \mathbf{b}.\mathbf{b}.$