Let a → = i ^ + 5 j ^ + α k ^ , b → = i ^ + 3 j ^ + β k ^ and c → = - i ^ + 2 j ^ - 3 k ^ be three vectors such that, | b → × c → | = 5 3 and a → is perpendicular to b → . Then the greatest amongst the values of | a → | 2 is ________.

Question

Let a → = i ^ + 5 j ^ + α k ^ , b → = i ^ + 3 j ^ + β k ^ and c → = - i ^ + 2 j ^ - 3 k ^ be three vectors such that, | b → × c → | = 5 3 and a → is perpendicular to b → . Then the greatest amongst the values of | a → | 2 is ________.,

MARKS App · Accepted Answer

a → · b → = 0 1 + 15 + α β = 0 α β = - 16 . . . ( 1 ) Also, b → × c → 2 = 75 10 + β 2 · 14 - 5 - 3 β 2 = 75 5 β 2 + 30 β + 40 = 0 β = - 4 , - 2 α = 4 , 8 a → m a x 2 = 26 + α 2 m a x = 90

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