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Vector Algebra

Question
CBSEENMA12036157

The vector straight a with rightwards arrow on top space equals space straight alpha space straight i with hat on top space plus 2 straight j with hat on top space plus straight beta straight k with hat on top lies in the plane of the vectors straight b with rightwards arrow on top space equals straight i with hat on top space plus straight j with hat on top space and space straight c with rightwards arrow on top space equals space straight j with hat on top space plus straight k with hat on top and bisects the angle between straight b with rightwards arrow on top space and space straight c with rightwards arrow on top.Then which one of the following gives possible values of α and β?

  • α = 2, β = 2

  • α = 1, β = 2

  • α = 2, β = 1

  • α = 2, β = 1

Solution

D.

α = 2, β = 1

straight a with rightwards arrow on top space equals space straight lambda left parenthesis straight b with hat on top space plus straight c with hat on top right parenthesis
rightwards double arrow space straight alpha space straight i with hat on top space plus 2 straight j with hat on top space plus straight beta straight k with hat on top space equals space straight lambda space open parentheses fraction numerator straight i with hat on top space plus 2 stack straight j space with hat on top plus straight k with hat on top over denominator square root of 2 end fraction close parentheses
straight lambda space equals space square root of 2 straight alpha space and space straight lambda space equals square root of 2
and space straight lambda space equals space square root of 2 straight beta
rightwards double arrow space straight alpha equals space 1 space and space straight beta space equals 1