JEE Main 2023 Mathematics question

Let a unit vector makes angles , , with the positive directions of the co-ordinate axes OX, OY, OZ respectively, where . If is perpendicular to the plane through points (1, 2, 3), (2, 3, 4) and (1, 5, 7), then which one of the following is true?

• (A) and
• (B) and
• (C) and Correct
• (D) and