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Question:

The vector(s) which is/are coplanar with vectors ^i+^j+2^k and ^i+2^j+^k, and perpendicular to the vector ^i+^j+^k is/are ^j−^k, ^i−^j, −^j+^k, −^i+^j

^j−^k

−^i+^j

^i−^j

−^j+^k

Solution:

Let →a=^i+^j+2^k, →b=^i+2^j+^k, →c=^i+^j+^k
Required vector, →v=λ[→c×(→a×→b)]=λ[(→c.→b)→a−(→c.→a)→b]
=λ[(4)^i+^j+2^k−(4)^i+2^j+^k]=λ[−^j+^k]
So, →v=−^j+^k or →v=^j−^k