If a = i + j + k, , ,b = i + j, , ,c = i and (a b) c = ,a + ,b, t… - Vidyadip

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 $b\,.\,c = 1$

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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