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Question

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

A
±^i+^j2^k6
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B
±^i+^j^k3
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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+^j2^k6
Given: a=^i^j,b=^j^k and c=^k^i, d is a unit vector such that ad=0=[bcd]
Let d=d1^i+d2^j+d3^k
ad=d1d2=0
d1=d2 (i)

And, [bcd]=0
∣ ∣011101d1d2d3∣ ∣=0
d3+d1+d2=0
d3=2d1 (ii)

where, d is a unit vector
(d1)2+(d2)2+(2d1)2=1
d1=±16
d=±^i+^j2^k6

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