find the equation of the line which satisfy the given condition: Passing through (2, 2√3) and inclined with the x-axis at an angle of 75o.

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

Given: point

$\left( \mathbf{2},\text{ }\mathbf{2}\surd \mathbf{3} \right)$

and

$\mathbf{\theta }\text{ }=\text{ }\mathbf{75}{}^\circ$

Condition of line:

$\left( \mathbf{y}\text{ }\text{ }\mathbf{-y1} \right)\text{ }=\text{ }\mathbf{m}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{-x1} \right)$

where,

$\mathbf{m}\text{ }=\text{ }\mathbf{incline}\text{ }\mathbf{of}\text{ }\mathbf{line}\text{ }=\text{ }\mathbf{tan}\text{ }\mathbf{\theta }\text{ }\mathbf{and}\text{ }\left( \mathbf{x1},\text{ }\mathbf{y1} \right)$

are the focuses through which line passes

$\therefore \mathbf{m}\text{ }=\text{ }\mathbf{tan}\text{ }\mathbf{75}{}^\circ$

$\mathbf{75}{}^\circ \text{ }=\text{ }\mathbf{45}{}^\circ \text{ }+\text{ }\mathbf{30}{}^\circ$

Applying the eqn:

We realize that the point (x, y) lies on the line with incline m through the decent point (x1, y1), if and provided that, its directions fulfill the condition

$\mathbf{y}\text{ }\text{ }\mathbf{-y1}\text{ }=\text{ }\mathbf{m}\text{ }\left( \mathbf{x}\text{ }\text{ }\mathbf{-x1} \right)$

Then, at that point,

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

$\mathbf{y}\text{ }\text{ }\mathbf{-2}\surd \mathbf{3}\text{ }=\text{ }\mathbf{2}\text{ }\mathbf{x}\text{ }\text{ }\mathbf{-4}\text{ }+\text{ }\surd \mathbf{3}\text{ }\mathbf{x}\text{ }\text{ }\mathbf{-2}\text{ }\surd \mathbf{3}$

$\mathbf{y}\text{ }=\text{ }\mathbf{2}\text{ }\mathbf{x}\text{ }\text{ }\mathbf{-4}\text{ }+\text{ }\surd \mathbf{3}\text{ }\mathbf{x}$

$\left( \mathbf{2}\text{ }+\text{ }\surd \mathbf{3} \right)\text{ }\mathbf{x}\text{ }\text{ }\mathbf{-y}\text{ }\text{ }\mathbf{-4}\text{ }=\text{ }\mathbf{0}$

∴ The condition of the line is

$\left( \mathbf{2}\text{ }+\text{ }\surd \mathbf{3} \right)\text{ }\mathbf{x}\text{ }\text{ }\mathbf{-y}\text{ }\text{ }\mathbf{-4}\text{ }=\text{ }\mathbf{0}.$

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.

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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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.

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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