Question

Find the measures of the angles between the following pairs of lines.

(i) x + y + 1 = 0, 2x + 3y + 7 = 0.

(ii) x + 3 = 0, x +
√3y-1=0


(iii) y – 1 = 0, 3x – √3
y + 4 = 0.​

Answer 1

Answer:

Step-by-step explanation:

3x+y−7=0 and x+2y+9=0

write in the form y=mx+c

i.e.y=−3x+7,y=  

2

−x

​  

−  

2

9

​  

 

∴m  

1

​  

=−3 and m  

2

​  

∓−  

2

1

​  

 

tan(A−B)=  

∣

∣

∣

∣

∣

​  

 

1+tanAtanB

tanA−tanB

​  

 

∣

∣

∣

∣

∣

​  

 

∣

∣

∣

∣

∣

​  

 

1+(−3)(−y  

2

​  

)

−3−(−y  

2

​  

)

​  

 

∣

∣

∣

∣

∣

​  

 

=  

∣

∣

∣

∣

∣

​  

 

5/2

−5/2

​  

 

∣

∣

∣

∣

∣

​  

=1

∴ Angle b/w then is tan  

−1

(1)=45  

∘

 

=  

4

π

​