Given points are:

⇒ A = (1,2,3)

⇒ B = (4,5,7)

⇒ C = (–4,3,–6)

⇒ D = (2,9,2)

Let us assume the direction ratios for line AB be (r₁,r₂,r₃) and CD be (r₄,r₅,r₆)

We know that direction ratios for a line passing through points (x₁, y₁, z₁) and (x₂, y₂, z₂) is (x₂–x₁, y₂–y₁, z₂–z₁).

Let’s find the direction ratios for the line AB

⇒ (r₁,r₂,r₃) = (4–1, 5–2, 7–3)

⇒ (r₁,r₂,r₃) = (3,3,4)

Let’s find the direction ratios for the line CD

⇒ (r₄,r₅,r₆) = (2–(–4), 9–3, 2–(–6))

⇒ (r₄,r₅,r₆) = (2+4, 9–3, 2+6)

⇒ (r₄,r₅,r₆) = (6,6,8)

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 the given two vectors is 0⁰.