a,b,c are three vectors such that (| a |= l ,| b |=2,| c |=3 ) and ( b . c = 0 ). If the projection of ( b ) along ( a ) is equal to the projection of ( c ) along ( a ), then (|2 a +3 b -3 c |= )

Step-by-step solution

Given, and ( gathered | a |=1,| b |=2,| c |=3 b c =0 gathered ) Now, (|2 a +3 b -3 c | ) ( gathered = 4| a |^2+9| b |^2+9| c |^2+12 a b -18 b c -12 a c = 4+9(4)+9(9)+12 a b -0-12 a c = 4+36+81+12 a b -12 a c gathered ) Since, projection of ( b ) along ( a ) is equal to projection of ( c ) along ( aligned a & a b = a c & = 121+6 a b -6 a b = 121 =11 aligned )