Question

Find the coordinates of the point which divides the line segment joining the points ( -2,3,5) and (1,- 4,6) in the ratio 2:3 internally . *​

Answer 1

☆ Given Question :-

Find the coordinates of the point which divides the line segment joining the points ( -2,3,5) and (1,- 4,6) in the ratio 2:3 internally .

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$\huge \orange{AηsωeR} ✍$

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$\begin{gathered}\begin{gathered}\bf given \: - \: \begin{cases} &\sf{A \: ( -2,3,5)} \\ &\sf{B \: (1,- 4,6)} \\ &\sf{C \: divides \: AB \: in \: 2 : 3} \end{cases}\end{gathered}\end{gathered}$

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$\begin{gathered}\begin{gathered}\bf \: To \: Find = \begin{cases} &\sf{coordinates \: of \: C} \\ \end{cases}\end{gathered}\end{gathered}$

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☆ Formula used :-

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Let us consider a line segment joining the points A and B,

$\sf \:  ⟼ A(x_1, \: y_1, \: z_1) \: and \: B(x_2, \: y_2,z_2)$

and let C(x, y, z) divides AB internally in the ratio m: n, then

C(x, y, z) is given by

$\sf \:  ⟼C(x, y, z) \: = (\dfrac{mx_2 + nx_1}{m + n} , \dfrac{my_2 + ny_1}{m + n} , \dfrac{mz_2 + nz_1}{m + n} )$

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$\large\underline\purple{\bold{Solution :- }}$

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☆ Let coordinates of A be B are ( -2,3,5)( and 1,- 4,6) nsk Let (x, y, z) be any coordinate qhich divides AB in hhe ratio m : n , then coordinates of C given by

$\sf \:  C(x, y, z) = (\dfrac{2 \times ( - 2) + 3 \times (1)}{2 + 3} , \dfrac{2 \times 3 + 3 \times ( - 4)}{23} , \dfrac{2 \times 5 + 3 \times 6}{2 + 3} )$

$\sf \:  ⟼C(x, y, z) = (\dfrac{ - 4 + 3}{5}, \dfrac{6 - 12}{5} , \dfrac{10 + 18}{5} )$

$\sf \:  ⟼\sf \:  ⟼C(x, y, z) = (\dfrac{ - 1}{5}, \dfrac{ - 6}{5} , \dfrac{28}{5} )$

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