Let us assume the direction ratios of vectors be (r₁,r₂,r₃) and (r₄,r₅,r₆).

Then,

⇒ (r₁,r₂,r₃) = (1,–2,1)

⇒ (r₄,r₅,r₆) = (4,3,2)

We know that the angle between the vectors with direction ratios proportional to (a₁,b₁,c₁) and (a₂,b₂,c₂) is given by:

⇒

Using the above formula we calculate the angle between the vectors.

Let be the angle between the two vectors given in the problem.

⇒

⇒

⇒

⇒

⇒

∴ The angle between two given vectors is .