R.E.F image î× (ĵ×k̂)+ĵ.(î×k̂) k̂.(î×î) =(î×î)+ĵ.( ĵ) k̂(0) =0 ĵ.ĵ 0 = | ĵ |^2 [∵ĵ×k̂=î,î×k̂= ĵ,î×î=0] = 1 ...

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Implicit Differentiation

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Question

Evaluate $^i \times (^j \times^k) +^j . (^i \times^k) -^k . (^i \times^i)$

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Solution

R.E.F image
$^i \times (^j \times^k) +^j . (^i \times^k) -^k . (^i \times^i)$
$= (^i \times^i) +^j . (-^j) -^k (0)$
$= 0 -^j .^j - 0$
$= - {∣ ∣^j ∣ ∣}^{2}$ $[∵^j \times^k =^i,^i \times^k = -^j,^i \times^i = 0]$
$= - 1$

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Similar questions

^i \times (^j \times^k) +^j \times (^k \times^i) +^k \times (^i \times^j) =

(^i +^j) \times^k

\to a =^i +^j +^k

\to b =^i +^j -^k

\to c =^i -^j +^k

\to d =^i -^j -^k

| (\to a \times \to b) . (\to c \times \to d) | =

\to a =^i +^j +^k; \to b =^i -^j +^k; \to c =^i +^j -^k

\to a =^i +^j +^k, \to b =^i +^j -^k

\to c =^i -^j +^k

\to d =^i -^j -^k

(\to a \times \to b) \times (\to c \times \to d) =

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