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Let a=hat(j)-hat(k) and b=hat(i)-hat(j)-...

Let `a=hat(j)-hat(k) and b=hat(i)-hat(j)-hat(k)`. Then, the vector v satisfying `atimesb+c=0 and a*b=3`, is

A

`hati-hatj-2hatk`

B

`hati+hatj-2hatk`

C

`-hati+hatj-2hatk`

D

`2hati-hatj+2hatk`

Text Solution

Verified by Experts

The correct Answer is:
C
We have
`vecaxxvecb+vecc=vec0`
`impliesvecc=vecbxxveca`
`impliesvecaxxvecc=vecaxx(vecbxxveca)`
`impliesvecaxxvecc=(veca.veca)vecb-(veca.vecb)veca`
`implies-2hati-hatj-hatk=2vecb-3(hatj-hatk)`
`implies2.vecb=-2hati+2hatj-4hatkimpliesvecb=-hati+hatj-2hatk`
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