JEE Main20248 Apr 2024Evening ShiftMathematicsVector AlgebraActual

Let a = i +2 j +3 k , b =2 i +3 j -5 k and c =3 i - j + k be three vectors. Let r be anit vector along b + c . If r a =3 , then 3 is equal to:

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Correct answer

C. 25

Step-by-step solution

aligned & r = k ( b + c ) & r a =3 & r a = k ( b a + c a ) & 3= k (2+6-15+3-2+3 ) aligned 3= k (-6+3 ) ...(1) r = k (5 i +2 j -(5- ) k )| r |=k 25+4+25+ ^2-10 =1 ...(2) k = 3 -6+3 = 1 -2+ put in (2) aligned & 4+ ^2-4 =54+ ^2-10 & 6 =50 & 3 =25 aligned

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