1.

The vector a=alpha hati+2hatj+betahatk lies in the plane of the vectors b=hati+hatj and c = hatj+hatk and bisects the angle between b and c. Then, which one of the following gives possible value of alpha and beta?

Answer»

`alpha=1, beta=1`
`alpha=2, beta=2`
`alpha=1, beta=2`
`alpha=2,beta=1`

Solution :Since, a, b, and C are coplanar.
`implies |(alpha,2,beta),(1,1,0),(0,1,1)|=0`
`implies alpha (1-0)-2(1-0)+beta (1-0)=0`
`implies alpha +beta =2` which is POSSIBLE for `alpha=1, beta =1`.


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