Question:
What is the acute angle between the lines x – 2 = 0 and √3x – y – 2 = 0?
What is the acute angle between the lines x – 2 = 0 and √3x – y – 2 = 0?
Options:
- 60°
- 0°
- 30°
- 45°
- 60°
- 0°
- 30°
- 45°
Correct Answer: c)
Explanation:
i Gi√en, lines are
z—2=0and√3z—-y—-2=0
‘ ⇒z=2andy=+3z—2
hon a
‘ Y y= V&-2 ‘
x: X
e
y eed
‘ Since, line x = 2 is a perpendicular line to the X-axis, so it makes angle 90°. ‘
B — _ z_ _Y¥Y_
‘ Line y = √3z 2or 5% 3 1 ‘
intercept positi√e X-axis and negati√e Y-axis and it makes an angle
‘ m = tan = /3 or § = 60° to the X-axis.
‘ In ΔABC, ZA + /B+ ZC = 180°
= 60° + 90° + ZC = 180°
= Z0=180° — 150° = 30° ‘
I 62.
1 daz? +y?>—2c-2y+1=0
‘
i Gi√en, lines are
z—2=0and√3z—-y—-2=0
‘ ⇒z=2andy=+3z—2
hon a
‘ Y y= V&-2 ‘
x: X
e
y eed
‘ Since, line x = 2 is a perpendicular line to the X-axis, so it makes angle 90°. ‘
B — _ z_ _Y¥Y_
‘ Line y = √3z 2or 5% 3 1 ‘
intercept positi√e X-axis and negati√e Y-axis and it makes an angle
‘ m = tan = /3 or § = 60° to the X-axis.
‘ In ΔABC, ZA + /B+ ZC = 180°
= 60° + 90° + ZC = 180°
= Z0=180° — 150° = 30° ‘
I 62.
1 daz? +y?>—2c-2y+1=0
‘