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The vector vec a=""alpha hat i+2 hat...

The vector ` vec a=""alpha hat i+2 hat j+""beta hat k` lies in the plane of the vectors ` vec b="" hat"i"+ hat j` and ` vec c= hat j+ hat k` and bisects the angle between ` vec b` and ` vec c` . Then which one of the following gives possible values of `alpha"and"beta` ? (1) `alpha=""2,beta=""2` (2) `alpha=""1,beta=""2` (3) `alpha=""2,beta=""1` (4) `alpha=""1,beta=""1`

A

`alpha=1, beta=1`

B

`alpha=2, beta=2`

C

`alpha=1, beta=2`

D

`alpha=2, beta=1`

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The correct Answer is:
D
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