Thevector ` 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 = 2, beta = 2 `B. `alpha = 1, beta = 2 `C. `alpha = 2, beta = 1 `D. `alpha = 1, beta = 1 `

Thevector ` vec a=""alpha hat i+2 hat j+""beta hat k`lies in the plane

1.	Thevector ` 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 = 2, beta = 2 `B. `alpha = 1, beta = 2 `C. `alpha = 2, beta = 1 `D. `alpha = 1, beta = 1 `
Answer» Correct Answer - D It is given that `veca` besects the angle between `vecb and vec c`. Therefore , `vec a` is parallel `(vec b + vec c )/(2)` So ` vec a = lambda (hat b + hat c ) ` `rArr alpha hati + 2 hatj + beta hatk = lambda ((hati + hatj ) /( sqrt(2))+(hatj + hatk )/(sqrt(2)))` `rArr alpha hati + 2 hatj + beta hatk = (lambda) /( sqrt(2)) (hati + 2 hat j + hatk ) ` `rArr alpha = (lambda )/(sqrt(2)) , 2 =sqrt(2) lambda and beta = (lambda )/(sqrt(2)) rArr alpha 1, beta =1`

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