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 A vector of magnitude 55 coplanar with vectors i^+2j^ and j^+2k^ and the  perpendicular vector 2^i+j^+2k^ is : 

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a
± 5 (5i∧     + 6j∧  −8k∧)
b
± 5 (5i∧     + 6j∧  −8k∧)
c
± 55 (5i∧     + 6j∧  −8k∧)
d
±  (5i∧     + 6j∧  −8k∧)

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detailed solution

Correct option is D

Unit vector coplanar with a→ and b→ and perpendicular to vector  c→  is  ± (a→ × b→) × ​c→|(a→ × b→ ) ×c→ |a→ × b→  =ijk120012 =i^ 4-0-j^ 2-0+k^1-0 =4i^-2j^+k^a→ ×b →×c→=ijk4-21212 = i^ -4-1-j^ 8-2+k^4+4=-5i^-6j^+8k^  a→ ×b →×c→=125 =55 ∴ unit vector of magnitude 55 coplanar is 55± a→ ×b →×c→55= ±5i^+6j^-8k^


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