Question: If $a = i + j + k,b = i + j,c = i$ and $(a \times b) \times c = \lambda a + \mu b$, then \(\lamb...

Question

If $a = i + j + k,b = i + j,c = i$ and $(a \times b) \times c = \lambda a + \mu b$ , then $\lambda + \mu =$

Answer 1

Solution

$\mathbf{a}.\mathbf{c} = 1$ and $\mathbf{b}.\mathbf{c} = 1$

Given that $(\mathbf{a} \times \mathbf{b}) \times \mathbf{c} = (\mathbf{c}.\mathbf{a})\mathbf{b} - (\mathbf{c}.\mathbf{b})\mathbf{a} = \mu\mathbf{b} + \lambda\mathbf{a}$

where $\mu = \mathbf{c}.\mathbf{a} = 1,\lambda = - (\mathbf{c}.\mathbf{b}) = - 1$

$\Rightarrow \mu + \lambda = 1 - 1 = 0$ .

Question: If \(a = i + j + k,b = i + j,c = i\) and \((a \times b) \times c = \lambda a + \mu b\), then \(\lamb...

Solution