The scalar product of the vector a unit vector along the sum of vectors and is equal to one. Find the value of λ.

Given: given vectors are

Then sum of vector is given by the resultant of .


Let the sum is .


Then





Then magnitude of is :





Scalar product of






Square on both sides:


⇒ (λ + 6)2 = (λ)2 + 4λ + 44


⇒ (λ)2 + 12λ + 36 =(λ)2 + 4λ + 44


⇒ 8λ = 8


⇒ λ = 1


16