Find the coordinates of the point which divides the line segment joining the points \[\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)\]and \[\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)\]in the ratio (i) \[\mathbf{2}:\text{ }\mathbf{3}\]internally, (ii) \[\mathbf{2}:\text{ }\mathbf{3}\]externally.

Find the coordinates of the point which divides the line segment joining the points

$\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)$

and

$\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)$

in the ratio (i)

$\mathbf{2}:\text{ }\mathbf{3}$

internally, (ii)

$\mathbf{2}:\text{ }\mathbf{3}$

externally.

Class 11 | Exercise 12.3 | Maths | NCERT | Three Dimensional Geometry

Find the coordinates of the point which divides the line segment joining the points

$\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)$

and

$\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)$

in the ratio (i)

$\mathbf{2}:\text{ }\mathbf{3}$

internally, (ii)

$\mathbf{2}:\text{ }\mathbf{3}$

externally.

Solution:

Let the line segment joining the points A

$\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)$

and B

$\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)$

be AB.

(i)

$\mathbf{2}:\text{ }\mathbf{3}$

internally

By using section formula,

So, the coordinates of the point which divides the line segment joining the points A

$\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)$

and B

$\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)$

in the ratio

$\mathbf{2}:\text{ }\mathbf{3}$

internally is given by:

Hence, the coordinates of the point which divides the line segment joining the points

$\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)$

and

$\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)$

$\left( -4/5,\text{ }1/5,\text{ }27/5 \right)$

(ii)

$\mathbf{2}:\text{ }\mathbf{3}$

externally

By using section formula,

So, the coordinates of the point which divides the line segment joining the points A

$\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)$

$\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)$

in the ratio

$\mathbf{2}:\text{ }\mathbf{3}$

externally is given by:

∴ The co-ordinates of the point which divides the line segment joining the points

$\left( \text{ }\mathbf{2},\text{ }\mathbf{3},\text{ }\mathbf{5} \right)$

) and

$\left( \mathbf{1},\text{ }\text{ }\mathbf{4},\text{ }\mathbf{6} \right)$

$\left( -8,\text{ }17,\text{ }3 \right)$

More Material

Find the angle between each of the following pairs of lines:

Find the coordinates of the foot of the perpendicular drawn from the point (1, 2, 3) to the line

Show that the lines and do not intersect each other.

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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More Material

Find the angle between each of the following pairs of lines:

Find the coordinates of the foot of the perpendicular drawn from the point (1, 2, 3) to the line

Show that the lines and do not intersect each other.

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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