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Question

A unit vector coplanar with i+j+2k and i+2j+k, and perpendicular to i+j+k, is

A
12(j+k)
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B
12(ki)
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C
12(ik)
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D
12(jk)
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Solution

The correct options are
A 12(j+k)
D 12(jk)
Let the required vector be pi+qj+rk
According to the condition of coplanarity, we have ∣ ∣112121pqr∣ ∣=0
2rq1(rp)+2(q2p)=0
2rqr+p+2q4p=0 or 3p+q+r=0
The vector is also perpendicular to i+j+k and so, p+q+r=0

Solving the two equations we have p=0 and q=r
This is satisfied by options A and D.

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