Solution:
Let the line segment joining the points A
![\[\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0adda3fe0ac17f8aa03c8923cc60645f_l3.png "Rendered by QuickLaTeX.com")
and B
![\[\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-75d0720435105f1c6905635a5d83b506_l3.png "Rendered by QuickLaTeX.com")
be AB.
(i)
![\[\mathbf{2}:\text{ }\mathbf{3}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a499d63c12c0dcb11e01e065feb57607_l3.png "Rendered by QuickLaTeX.com")
internally
By using section formula,
So, the coordinates of the point which divides the line segment joining the points A
and B
in the ratio
internally is given by:
Hence, the coordinates of the point which divides the line segment joining the points
and
is
![\[\left( -4/5,\text{ }1/5,\text{ }27/5 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-722d3e8d26c9a2d36b5b7277b3c96292_l3.png "Rendered by QuickLaTeX.com")
(ii)
externally
By using section formula,
So, the coordinates of the point which divides the line segment joining the points A
B
in the ratio
externally is given by:
∴ The co-ordinates of the point which divides the line segment joining the points
) and
is
![\[\left( -8,\text{ }17,\text{ }3 \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-70155364a7a336a5be944853478c9b21_l3.png "Rendered by QuickLaTeX.com")
