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Question

Leta=^i^j,b=^j^k,c=^k^i. If d is a unit vector such that ad=0=[bcd], then d

A
(^i+^j2^k)6
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B
(^i+^j2^k)6
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C
(^i^j+2^k)6
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D
(^i+^j+2^k)6
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Solution

The correct options are
A (^i+^j2^k)6
C (^i^j+2^k)6
Let d=xi+yj+zk
Given that a.d=xy=0 ...(1)
and [bcd]=∣ ∣011101xyz∣ ∣=(zx)(y)=x+y+z=0
Using (1): z=2x
Since, x2+y2+z2=1
Therefore, x2+y2+4x2=1
x=±16
Therefore, d=±(^i+^j2^k)6

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