If then is equal to

Question

Question

This question was previously asked in

UP TGT Mathematics 2021 Official Paper

Answer 1

Given:

Concept:

î × î = ĵ × ĵ = k̂ × k̂ = 0

î × ĵ = k̂ , ĵ × k̂ = î , k̂ × î = ĵ

Calculation:

Let a = mî + nĵ +lk̂

According to the Question

= î × (mî + nĵ +lk̂ × î) + ĵ × (mî + nĵ +lk̂ × ĵ) + k̂ × (mî + nĵ +lk̂ × k̂)

= î × (-nk̂ + lĵ) + ĵ × (mk̂ -lî ) + k̂ × (-mĵ + nî)

= nĵ + lk̂ + mî + lk̂ + mî + nĵ

= 2(mî + nĵ +lk̂ ) = 2

∴ The correct option is 3

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