Question

What is angle between x = 2 and x - 3 y = 6

Answer 1

Answer:

π/2 - tan⁻¹ ( 1/3 ) or Cot⁻¹ ( 1/3 )

Step-by-step explanation:

Given----> x = 2 and x - 3y = 6

To find------> Angle between given lines

Solution---->

1) Plzzz see the attachment

2) If we see the first equation it is of the form

x = m , these type of lines are parallel to y axis and at a distance of m from y axis so first line is parallel to y axis and at a distance of 2 unit from y axis and make right angle from x axis

3) Now if we change second equationo in intercept form we find that , line 2 cut positive intercept on x axis and negative intercept on y axis respectively

4) Then we find slope of 2nd line then we easily calculate angle between by anglesum property of triangle .

Answer 2

Answer:

$\large\boxed{\sf{{ \tan }^{ - 1} 3}}$

Step-by-step explanation:

Given lines :

• x = 2
• x - 3y = 6

Resolving these equations of lines :

• x - 0y - 2 = 0
• x - 3y - 6 = 0

Clearly these are in the form:

• $a_{1}x+b_{1}y+c_{1}=0$
• $a_{2}x+b_{2}y+c_{2}=0$

Let the acute angle between these lines is $\theta$

Therefore, the angle is given by:

$\large \boxed{ \red{\tan \theta = | \dfrac{a_{1}b_{2} - b_{1}a_{2}}{a_{1}a_{2} + b_{1}b_{2}} | }}$

$= > \tan \theta = | \frac{( - 3 \times 1) -( 0 \times 1) }{(1 \times 1) + ( - 3 \times 0)} | \\ \\ = > \tan \theta = | \frac{ - 3 - 0}{1 - 0} | \\ \\ = > \tan \theta = | \frac{ - 3}{1} | \\ \\ = > \tan \theta = | - 3| \\ \\ = > \tan \theta = 3 \\ \\ = > \sf{ \blue{\theta = { \tan }^{ - 1} 3}}$