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

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