The scalar product of vectors a = i +2 j + k and a unit vector along the sum of vectors b =2 i -4 j +5 k and c = i +2 j -3 k is one, then the value of is

Step-by-step solution

aligned & b + c =(2+ ) i -2 j +2 k & Unit vector = b + c b + c & = (2+ ) i -2 j +2 k (2+ )^2+(-2)^2+2^2 & = (2+ ) i -2 j +2 k ^2+4 +12 aligned According to the given condition, aligned & ( i +2 j + k ) ( (2+ ) i -2 j +2 k ^2+4 +12 )=1 & (2+ )-4+2 ^2+4 +12 =1 & = ^2+4 +12 & ^2= ^2+4 +12 & 4 =-12 & =-3 aligned