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Question

Let a=ij,b=jk,c=ki. If d is a unit vector such that ad=[b c d]=0, then d is equal to

A
±i+j2k6
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B
±i+jk3
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C
±i+j+k3
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D
±k
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Solution

The correct option is A ±i+j2k6
Let d=x^i+y^j+z^k
ad=0x=y (i)
[b c d]=∣ ∣011101xyz∣ ∣=(zx)(y)
x+y+z=0
Using (i), we get
z=2x (ii)
Since d is unit vector
x2+y2+z2=1(iii)
Using (i),(ii) and (iii), we get
x=±16
d=±i+j2k6

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