If a , b , c are three vectors such that a 0 , | a | = | c | = 1, | b | = 4 and | b c | = 15 . If b - 2 c = a then ^2 equals:

Step-by-step solution

Using Lagrange's identity: | b c |^2 + ( b c )^2 = | b |^2| c |^2 15 + ( b c )^2 = 16 b c = 1 From b - 2 c = a , squaring both sides: | b |^2 + 4| c |^2 - 4( b c ) = ^2| a |^2 16 + 4 - 4( b c ) = ^2 ^2 = 20 - 4( b c ) For b c = 1 : ^2 = 16 (not in options) For b c = -1 : ^2 = 24 ^2 = 24