Question

Find the slope and the inclination of the line AB if:
(ii) $A=(-1,2,\sqrt{3})\text{and}B=(-2,\sqrt{3})$

Answer 1

Finding the slope of line AB
Let $A(-1,2\sqrt{3})=(x_1,y_1)\text{and}B(-2,\sqrt{3})=(x_2,y_2)$.

We know that,

Slope of line AB $=\frac{y_2-y_1}{x_2-x_1}$

$=\frac{\sqrt{3}-2\sqrt{3}}{-2-(-1)}$

$=\frac{-\sqrt{3}}{-2+1}$

$=\frac{-\surd 3}{-1}$

$\therefore$ Slope of line AB$=\sqrt{3}$

Finding the inclination of line AB
Let inclination of line AB be ${\theta }^{\circ }$.
$\therefore \text{tan}\theta =$ Slope of line AB
$\Rightarrow \text{tan}\theta =\sqrt{3}$
$\Rightarrow \text{tan}\theta =\text{tan}{60}^{\circ }$
$\therefore \theta ={60}^{\circ }$
Hence, the slope of a line AB is $\sqrt{3}$ and inclination is ${60}^{\circ }$.