Find the coordinates of the point which divides the joint of `P(2,-1,4)a n dq(4,3,2)` in the ratio 2:3 (i) internally (ii) externally.

Explanation

To find the coordinates of the point that divides the line segment joining points \( P(2, -1, 4) \) and \( Q(4, 3, 2) \) in the ratio \( 2:3 \), we will solve the problem in two parts: (i) internally and (ii) externally.

### Part (i): Internal Division

The formula for finding the coordinates of a point that divides the line segment joining points \( P(x_1, y_1, z_1) \) and \( Q(x_2, y_2, z_2) \) in the ratio \( m_1:m_2 \) internally is given by:

\[
\left( \frac{m_1 x_1 + m_2 x_2}{m_1 + m_2}, \frac{m_1 y_1 + m_2 y_2}{m_1 + m_2}, \frac{m_1 z_1 + m_2 z_2}{m_1 + m_2} \right)
...