find the equation of the line which satisfy the given condition: Passing through (0, 0) with slope m.

Class 11 | Exercise 10.2 | Maths | NCERT | Straight Lines

Given:

Point (0, 0) and slant, \[\mathbf{m}\text{ }=\text{ }\mathbf{m}\]

We realize that the point (x, y) lies on the line with slant m through the decent point (x0, y0), if and provided that, its directions fulfill the condition \[\mathbf{y}\text{ }\text{ }\mathbf{y0}\text{ }=\text{ }\mathbf{m}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{x0} \right)\]

In this way, \[\mathbf{y}\text{ }\text{ }\mathbf{0}\text{ }=\text{ }\mathbf{m}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{0} \right)\]

\[\mathbf{y}\text{ }=\text{ }\mathbf{mx}\]

\[\mathbf{y}\text{ }\text{ }\mathbf{mx}\text{ }=\text{ }\mathbf{0}\]

∴ The condition of the line is \[\mathbf{y}\text{ }\text{ }\mathbf{mx}\text{ }=\text{ }\mathbf{0}.\]

i

Find the vector equation of the line passing through the point with position vector and parallel to the vector Deduce the Cartesian equations of the line.

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A line passes through the point (3, 4, 5) and is parallel to the vector Find the equations of the line in the vector as well as Cartesian forms.

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{x}{{|x|}},x \ne 0\\ 0,x = 0 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 0} f(x) \end{array}$ does not exist.

Let $\begin{array}{l} f(x) = \left\{ \begin{array}{l} \frac{|x-3|}{{(x-3)’}},x \ne 3\\ 0,x = 3 \end{array} \right.\\ \end{array}$ . Show that $\begin{array}{l} \mathop {\lim }\limits_{x \to 3} f(x) \end{array}$ does not exist.

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