The coordinates of the point which divides th | vedclass

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(D) Let the points be $A(2, -1, 3)$ and $B(4, 3, 1)$. The ratio is $m_1 : m_2 = 3 : 4$.Using the section formula for internal division:$x = \frac{m_1

Vedclass · Accepted Answer

$(\frac{20}{7}, \frac{5}{7}, \frac{15}{7})$

Vedclass · Answer

(D) Let the points be $A(2, -1, 3)$ and $B(4, 3, 1)$. The ratio is $m_1 : m_2 = 3 : 4$.Using the section formula for internal division:$x = \frac{m_1 x_2 + m_2 x_1}{m_1 + m_2} = \frac{3(4) + 4(2)}{3 + 4} = \frac{12 + 8}{7} = \frac{20}{7}$$y = \frac{m_1 y_2 + m_2 y_1}{m_1 + m_2} = \frac{3(3) + 4(-1)}{3 + 4} = \frac{9 - 4}{7} = \frac{5}{7}$$z = \frac{m_1 z_2 + m_2 z_1}{m_1 + m_2} = \frac{3(1) + 4(3)}{3 + 4} = \frac{3 + 12}{7} = \frac{15}{7}$Thus,the coordinates are $(\frac{20}{7}, \frac{5}{7}, \frac{15}{7})$.Therefore,the correct option is $D$.

The coordinates of the point which divides the line segment joining the points $(2, -1, 3)$ and $(4, 3, 1)$ in the ratio $3 : 4$ internally are given by:

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