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