Let $\mathrm{A}(\alpha, 4,7)$ and $\mathrm{B}(3, \beta, 8)$ be two points in space. If YZ plane and ZX plane respectively divide the line segment joining the points A and B in the ratio $2: 3$ and 4:5, then the point C which divides $\overline{\mathrm{AB}}$ in the ratio $\alpha: \beta$ externally is

• A

  $\left(\frac{16}{3}, 10,3\right)$
• B

  $\left(\frac{-16}{3}, \frac{28}{3}, \frac{19}{3}\right)$
• C

  $\left(\frac{-16}{3}, \frac{-28}{3}, \frac{-19}{3}\right)$
• Correct answer
  D

  $\left(\frac{-16}{3}, 10, \frac{19}{3}\right)$

Hence, the correct answer is option: 'D'.