The scalar product of the vector i + j + k with a unit vector along the sum of the vectors 2 i +4 j -5 k and i +2 j +3 k is equal to 1 , then value of is

Step-by-step solution

(2 i +4 j -5 k )+( i +2 j +3 k )=(2+ ) i +6 j -2 k Unit vector along the above vector is (2+ ) i +6 j -2 k (2+ )^2+6^2+(-2)^2 = (2+ ) i +6 j -2 k ^2+4 +44 Scalar product of ( i + j + k ) with this unit vector is 1 . aligned & ( i + j + k ) (2+ ) i +6 j -2 k ^2+4 +44 =1 & (2+ )+6-2 ^2+4 +44 =1 & ^2+4 +44 = +6 & ^2+4 +44=( +6)^2 & 8 =8 & =1 aligned