projection of a on b is given by:

|| = (2² + 6² + 3²)^1/2

⇒|| = (4 + 36 + 9)^1/2 = (49)^1/2 = 7

a unit vector in the direction of the sum of the vectors is given by:

Now it is given that:

⇒

⇒2 λ + 6 + (3×4) = 28

⇒ λ = (28 - 12 - 6)/2

⇒ λ = 10/2 = 5

Ans: λ = 5