find the equation of the line which satisfy the given condition: Intersecting the x-axis at a distance of 3 units to the left of origin with slope –2.

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

Given:

Incline, \[\mathbf{m}\text{ }=\text{ }-\text{ }\mathbf{2}\]

We realize that assuming a line L with incline m makes x-capture d, condition of L is

\[\mathbf{y}\text{ }=\text{ }\mathbf{m}\left( \mathbf{x}\text{ }-\text{ }\mathbf{d} \right).\]

In the event that the distance is 3 units to one side of beginning, \[\mathbf{d}\text{ }=\text{ }-\text{ }\mathbf{3}\]

In this way, \[\mathbf{y}\text{ }=\text{ }\left( -\text{ }\mathbf{2} \right)\text{ }\left( \mathbf{x}\text{ }\text{ }\left( -\text{ }\mathbf{3} \right) \right)\]

\[\mathbf{y}\text{ }=\text{ }\left( -\text{ }\mathbf{2} \right)\text{ }\left( \mathbf{x}\text{ }+\text{ }\mathbf{3} \right)\]

\[\mathbf{y}\text{ }=\text{ }-\text{ }\mathbf{2x}\text{ }\text{ }\mathbf{6}\]

\[\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }+\text{ }\mathbf{6}\text{ }=\text{ }\mathbf{0}\]

∴ The condition of the line is \[\mathbf{2x}\text{ }+\text{ }\mathbf{y}\text{ }+\text{ }\mathbf{6}\text{ }=\text{ }\mathbf{0}.\]

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.

A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

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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A line passes through the point (2, 1, -3) and is parallel to the vector Find the equations of the line in vector and Cartesian forms.

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.

Evaluate:

Evaluate:

Evaluate:

If $f(x) = |x| – 3,find\mathop {\lim }\limits_{x \to 3} f(x)$

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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