Reduce the following equations into intercept form and find their intercepts on the axes. (iii) 3y + 2 = 0

Class 11 | Exercise 10.3 | Maths | NCERT | Straight Lines

\[\left( \mathbf{iii} \right)\text{ }\mathbf{3y}\text{ }+\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{0}\]

Given:

The condition is \[\mathbf{3y}\text{ }+\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{0}\]

Condition of line in capture structure is given by\[\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{1}\] , where ‘a’ and ‘b’ are blocks on x pivot and y – hub separately.

In this way, \[\mathbf{3y}\text{ }=\text{ }-\text{ }\mathbf{2}\]

Presently, let us partition the two sides by – 2, we get

\[\mathbf{3y}/\text{ }-\text{ }\mathbf{2}\text{ }=\text{ }-\text{ }\mathbf{2}/\text{ }-\text{ }\mathbf{2}\]

\[\mathbf{3y}/\text{ }-\text{ }\mathbf{2}\text{ }=\text{ }\mathbf{1}\]

\[\mathbf{y}/\left( -\text{ }\mathbf{2}/\mathbf{3} \right)\text{ }=\text{ }\mathbf{1}\]

∴ The above condition is of the structure\[\mathbf{x}/\mathbf{a}\text{ }+\text{ }\mathbf{y}/\mathbf{b}\text{ }=\text{ }\mathbf{1}\] , where \[\mathbf{a}\text{ }=\text{ }\mathbf{0},\text{ }\mathbf{b}\text{ }=\text{ }-\text{ }\mathbf{2}/\mathbf{3}\]

Capture on x – axis is\[~\mathbf{0}\]

Capture on y – axis is \[-\text{ }\mathbf{2}/\mathbf{3}\]

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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