![\[\left( \mathbf{4},\text{ }\mathbf{2},\text{ }\text{ }\mathbf{6} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-7b2b319c83af0f4415dd9c78671ae2e7_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{10},\text{ }\mathbf{16},\text{ }\mathbf{6} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b9fc798b7f04b8225ee220ac04bcf0cd_l3.png "Rendered by QuickLaTeX.com")
Consider A \[({{x}_{1}},\text{ }{{y}_{1}},\text{ }{{z}_{1}})\]and B \[({{x}_{2}},\text{ }{{y}_{2}},\text{ }{{z}_{2}})\]trisect the line segment joining the points P \[\left( \mathbf{4},\text{...
![\[\left( \mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{4} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-199d64e6806536c1b3cb857efe67f5ed_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{1},\text{ }\mathbf{2},\text{ }\mathbf{1} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dfc9b15e84c73dbb78d47bc9d461ffe2_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{0},\text{ }\mathbf{1}/\mathbf{3},\text{ }\mathbf{2} \right)~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0ebe890b071a03a5f762eef8bc17b94e_l3.png "Rendered by QuickLaTeX.com")
Consider the point P divides AB in the ratio \[k:\text{ }1\]. By using section formula, So we have, Now, we check if for some value of k, the point coincides with the point C. Put \[\left( -k+2...
![\[\left( -\mathbf{2},\text{ }\mathbf{4},\text{ }\mathbf{7} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-8b71485cf20e82a2a5a637c3422e2109_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{3},-\text{ }\mathbf{5},\text{ }\mathbf{8} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-05e14e4f32602279f3ac57eb034e0e97_l3.png "Rendered by QuickLaTeX.com")
Solution: Let the line segment formed by joining the points A \[\left(-\mathbf{2},\text{ }\mathbf{4},\text{ }\mathbf{7} \right)\]and B \[\left( \mathbf{3},-\text{ }\mathbf{5},\text{ }\mathbf{8}...
![\[\left( \mathbf{3},\text{ }\mathbf{2},\text{ }\text{ }\mathbf{4} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0b789d716677da76a2f2575aa3db7ee5_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{5},\text{ }\mathbf{4},\text{ }\text{ }\mathbf{6} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-bc05994728fe8c2319e9d7d4c55a3235_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{9},\text{ }\mathbf{8},\text{ }\mathbf{10} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1f5aaf3ddebde616540844806ed2797f_l3.png "Rendered by QuickLaTeX.com")
Solution: Let us consider B divides AC in the ratio \[k:\text{ }1\]. By using section formula, So, we have \[9k\text{ }+\text{ }3\text{ }=\text{ }5\text{ }\left( k+1 \right)\] \[9k\text{ }+\text{...
![\[\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-0adda3fe0ac17f8aa03c8923cc60645f_l3.png "Rendered by QuickLaTeX.com")
![\[\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-75d0720435105f1c6905635a5d83b506_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{2}:\text{ }\mathbf{3}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a499d63c12c0dcb11e01e065feb57607_l3.png "Rendered by QuickLaTeX.com")
Solution: Let the line segment joining the points A \[\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)\]and B \[\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6}...