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The coordinates of the points A and B are (2, 5, 4) and (2, 1, 8) respectively.

The coordinates of the points A and B are (2, 5, 4) and (2, 1, 8) respectively. In what ratio does the point C(2, 4, 5) divide AB?

Answers

Raphael
AC = OC - OA

$ \begin{pmatrix}
2 \\
4 \\
5
\end{pmatrix} - \begin{pmatrix}
2 \\
5 \\
4
\end{pmatrix} = \begin{pmatrix}
0 \\
-1 \\
1
\end{pmatrix}$

CB = OB - OC

$ \begin{pmatrix}
2 \\
1 \\
8
\end{pmatrix} - \begin{pmatrix}
2 \\
4 \\
5
\end{pmatrix} = \begin{pmatrix}
0 \\
-3 \\
3
\end{pmatrix}$

AC = kCB

$ \begin{pmatrix}
0 \\
-1 \\
4
\end{pmatrix} =k \begin{pmatrix}
0 \\
-3 \\
3
\end{pmatrix}$

k =$\frac{1}{3}$

AC = $\frac{1}{3}CB$

AC:CB = 1:3
raphael answered the question on January 14, 2017 at 07:28

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