MCQ
If $a = i + j + k,\,\,b = i + j,\,\,c = i$ and $(a \times b) \times c = \lambda \,a + \mu \,b$, then $\lambda + \mu = $
- ✓$0$
- B$1$
- C$2$
- D$3$
✓
Answer
Correct option: A.
$0$
a
(a) $a\,.\,c = 1$ and $b\,.\,c = 1$
(a) $a\,.\,c = 1$ and $b\,.\,c = 1$
Given that $(a \times b) \times c = (c\,.\,a)b - (c\,.\,b)\,a = \mu \,b + \lambda a$
where $\mu = c\,.\,a = 1,\,\,\lambda = - \,(c\,.\,b) = - \,1$
$ \Rightarrow \,\,\mu + \lambda = 1 - 1 = 0$.
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