Let the vectors a , b , c be such that | a |=2,| b |=4 and | c |=4 . If the projection of b on a is equal to the projection of c on a and b is perpendicular to c , then the value of | a + b - c | is equal to

Step-by-step solution

|| a |=2,| b |=4 and | c =4 According to the given condition, ( Projection of b on a )=( Projection of c on a ) array ll & b a | a | = c a | a | & b a = c a & ( ~b - c ) a =0 ...(i) array Now consider, | a + b - c | aligned & = | a + b - c |^2 & = | a |^2+| b - c |^2+2 a ( b - c ) & = (2)^2+| b - c |^2+0 aligned ...[from(ii)] aligned & = 4+| b |^2+| c |^2-2( ~b c ) & = 4+(4)^2+(4)^2+0 aligned [ b and c are perpendicular ] aligned & = 36 & =6 aligned