Consider three vectors a , b , c . Let | a |=2,| b |=3 and a = b c . If [0, 3 ] is the angle between the vectors b and c , then the minimum value of 27| c - a |^2 is equal to:

Step-by-step solution

aligned & | c - a |=| c |^2+| a |^2-2 a c & =| c |^2+4-0 & a = b c & | a |=| b c | & 2=3| c | & | c |= 2 3 cosec [0, 3 ] & | c |_ = 2 3 2 3 cosec [ 2 3 , ) & 27| c - a |_ ^2=27 ( 16 27 +4 )=124 aligned