If a =2 i +3 j +2 k , b =2 i + j - k and c = i +3 j are such that ( a + b ) is perpendicular to c , then the value of is

Step-by-step solution

Let d = a + b aligned d & =(2 i +3 j +2 k )+ (2 i + j - k ) & =2 i +3 j +2 k +2 i + j - k & =(2 +2) i +(3+ ) j +(2- ) k aligned Now, d is perpendicular to c . aligned & c d =0 & ( i +3 j ) [(2 +2) i +(3+ ) j +(2- ) k ]=0 & 1(2 +2)+3(3+ )=0 & 2 +2+9+3 =0 & 5 +11=0 & = -11 5 aligned