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If a=î+ĵ+k̂,b...

Question

$If \to a =^i +^j +^k, \to b =^i +^j, \to c =^i and (\to a \times \to b) \times \to c = λ \to a + μ \to b,$ then the value of $λ + μ$ is

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Solution

Given, $(\to a \times \to b) \times \to c = λ \to a + μ \to b$
$\Rightarrow (\to a \cdot \to c) \to b - (\to b \cdot \to c) \to a = λ \to a + μ \to b$
By comparing, we get
$\Rightarrow λ = - (\to b \cdot \to c), μ = (\to a \cdot \to c)$
On substituting $\to a, \to b, \to c,$ we have,
$\Rightarrow λ = - ((^i +^j) \cdot (^i)), μ = ((^i +^j +^k) \cdot (^i))$
$\Rightarrow λ = - 1, μ = 1 \Rightarrow λ + μ = - 1 + 1 = 0$

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Standard XII Physics

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