Question

The resultant of vectors OA and OB is perpendicular to OA (figure 2-W5) Find the angle AOB .​

Answer 1

Answer:

∠AOB = 131.8°

Explanation:

The resultant of vectors OA and OB is perpendicular to OA

Resultant = OA + OB

let say x = i  & y = j

OA = 4 i  + 0j

OB = 6Cosθ i  + 6Sinθj

OA + OB =  4 i  + 0j  + 6Cosθ i  + 6Sinθj

=> OA + OB = (4 + 6Cosθ)i + 6Sinθj

Now OA + OB  ⊥ OA

=> OA + OB have only j component

=> 4 + 6Cosθ = 0

=> 2 + 3Cosθ = 0

=> Cosθ = -2/3

=> θ = 131.8°

∠AOB = 131.8°