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STD 12 - 10. vector algebra — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 12 - 10. vector algebra4 Marks
Question
If $a = i + j + k,\,\,b = i + j,\,\,c = i$ and $(a \times b) \times c = \lambda \,a + \mu \,b$, then $\lambda + \mu = $
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Answer

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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