JEE Main | 2018VectorHard

Question

Let u→ be a vector coplanar with the vectors a→=2i^+3j^-k^ and b→=j^+k^. If u→ is perpendicular to a→and u→.b→= 24, then |u→|2 is equal to- 

Options

A.

315

B.

256

C.

84

D.

336

Solution

u→=λ(a→×b→)×a→
=λ{a→2.b→-(a→.b→)a→}
=λ{–4i^+8j^+16k^}
u→=λ' {-i^+2j^+4k^}
u→.b→=24
⇒ λ' =4
u→=-4i^+8j^+16k^
u→=336

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