If a-2-k-b-2-2k-c-2k- and a- b-c -1- - 1- - 1- 1- k- then the value of -3- is

We know thata× (b×c)=(a·c)(b) (a·b)(c) =5(î+2ĵ+2k̂) 6(î+ĵ+2k̂) = î+4ĵ 2k̂ ⇒a× (b×c)= (1+α )î+β (1+α )ĵ+γ (1+α )(1+β )k̂= î+4ĵ 2k̂ By comparing, we get ⇒ nbsp; ...

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Byju's Answer

Standard XII

Physics

Subtraction of a Vector

If a=2î+ĵ+k̂,...

Question

If $\to a = 2^i +^j +^k, \to b =^i + 2^j + 2^k, \to c =^i +^j + 2^k$ and $\to a \times (\to b \times \to c) =$
$(1 + α)^i + β (1 + α)^j + γ (1 + α) (1 + β)^k$ , then the value of $α - β - 3 γ$ is

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Solution

We know that $\to a \times (\to b \times \to c) = (\to a \cdot \to c) (\to b) - (\to a \cdot \to b) (\to c) = 5 (^i + 2^j + 2^k) - 6 (^i +^j + 2^k) = -^i + 4^j - 2^k$
$\Rightarrow \to a \times (\to b \times \to c) = (1 + α)^i + β (1 + α)^j + γ (1 + α) (1 + β)^k = -^i + 4^j - 2^k$
By comparing, we get
$\Rightarrow 1 + α = - 1, β (1 + α) = 4, γ (1 + α) (1 + β) = - 2$
$α = - 2, β (- 1) = 4 \Rightarrow β = - 4 \Rightarrow γ (- 1) (1 - 4) = - 2$
$\Rightarrow γ (- 1) (- 3) = - 2 \Rightarrow γ = \frac{- 2}{3}$
$\Rightarrow α - β - 3 γ = - 2 + 4 + 2 = 4$

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If →a=2^i+^j+^k,→b=^i+2^j+2^k,→c=^i+^j+2^k and →a×(→b×→c)= (1+α)^i+β(1+α)^j+γ(1+α)(1+β)^k, then the value of α−β−3γ is

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$(1 + α)^i + β (1 + α)^j + γ (1 + α) (1 + β)^k$ , then the value of $α - β - 3 γ$ is