Given:
![\[\mathbf{p}\text{ }=\text{ }\mathbf{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-a1a2d148a8aed2024d6a25a1f55560ee_l3.png "Rendered by QuickLaTeX.com")
and
![\[\mathbf{\omega }\text{ }=\text{ }\mathbf{30}{}^\circ \]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-77ff3e48ad27bb4a6fe007ced823e682_l3.png "Rendered by QuickLaTeX.com")
We realize that the condition of the line having typical distance p from the beginning and point ω which the ordinary makes with the positive heading of x-axis is given by
![\[\mathbf{x}\text{ }\mathbf{cos}\text{ }\mathbf{\omega }\text{ }+\text{ }\mathbf{y}\text{ }\mathbf{sin}\text{ }\mathbf{\omega }\text{ }=\text{ }\mathbf{p}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-dfe5019c6f69af8efaf01e6975d8e6b3_l3.png "Rendered by QuickLaTeX.com")
Subbing the qualities in the situation, we get
![\[\mathbf{x}\text{ }\mathbf{cos30}{}^\circ \text{ }+\text{ }\mathbf{y}\text{ }\mathbf{sin30}{}^\circ \text{ }=\text{ }\mathbf{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-b3547e2c789c95a63abf411afd7fde47_l3.png "Rendered by QuickLaTeX.com")
![\[\mathbf{x}\left( \surd \mathbf{3}/\mathbf{2} \right)\text{ }+\text{ }\mathbf{y}\left( \text{ }\mathbf{1}/\mathbf{2}\text{ } \right)\text{ }=\text{ }\mathbf{5}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-65449b4b67899d6893c4e37d4722fb0c_l3.png "Rendered by QuickLaTeX.com")
![\[\surd \mathbf{3}\text{ }\mathbf{x}\text{ }+\text{ }\mathbf{y}\text{ }=\text{ }\mathbf{5}\left( \mathbf{2} \right)\text{ }=\text{ }\mathbf{10}~~~~~~~~\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-e0e59404f67326b357c69ab44b339876_l3.png "Rendered by QuickLaTeX.com")
![\[\surd \mathbf{3}\text{ }\mathbf{x}\text{ }+\text{ }\mathbf{y}\text{ }\text{ }\mathbf{-10}\text{ }=\text{ }\mathbf{0}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-d05144d09fc770004104cc7bf4bb792c_l3.png "Rendered by QuickLaTeX.com")
∴ The condition of the line is
![\[\surd \mathbf{3}\text{ }\mathbf{x}\text{ }+\text{ }\mathbf{y}\text{ }\text{ }\mathbf{-10}\text{ }=\text{ }\mathbf{0}.\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-1db0b109e6030a83fd6163fef8ab0dfc_l3.png "Rendered by QuickLaTeX.com")
