Question

find the angle between the lines x=2 y=3​

Answer 1

Given :

The line equation as

 x = 2

And

 y = 3

To Find :

The angle between the lines

Solution :

As The line equation is x = 2  and y = 3

So, For  x = 2 , y = 0

And for y = 3 , x = 0

∴  Points are $x_1 , y_1$  = 2 , 0

And   $x_2, y_2$  = 0 , 3

Now, slope of line is written as

 Slope = m = $\dfrac{y_2-y_1}{x_2-x_1}$

Or,          m = $\dfrac{3-0}{0-2}$

∴             m = $\dfrac{3}{-2}$

i.e slope = m = - $\dfrac{3}{2}$

Hence, The slope of the line is  - $\dfrac{3}{2}$    Answer

Answer 2

Answer:

Let us find the angle of $x=2$ wrt x axis first.

$y=mx+c\\0y=1x-2\\y=\frac{x-2}{0} \\m=\frac{1}{0}\\m=infinity\\m=tan(\alpha )\\\alpha =arctan(infinity)=90^o$

Now, let do it for $y=3$.

$y=mx+c\\y=0x=c\\m=0\\m=tan(\beta )\\\beta =arctan(0)\\\beta =0^o$

Angle between the lines

$=|\beta -\alpha |\\=|90-0|\\=|90|\\=90^o$

Hope it helps.