Find the angle between each of the following pairs of straight lines:

1.	Find the angle between each of the following pairs of straight lines: (i) 3x+y+12=0 and x+2y−1=0 (ii) 3x−y+5=0 and x−3y+1=0 (iii) 3x+4y−7=0 and 4x−3y+5=0 (iv) x−4y=3 and 6x−y=11 (v) (m2−mn)y=(mn+n2)x+n2 and (mn+m2)y=(mn+n2)x+m3.
Answer» Find the angle between each of the following pairs of straight lines: (i) $3 x + y + 12 = 0$ and $x + 2 y - 1 = 0$ (ii) $3 x - y + 5 = 0$ and $x - 3 y + 1 = 0$ (iii) $3 x + 4 y - 7 = 0$ and $4 x - 3 y + 5 = 0$ (iv) $x - 4 y = 3$ and $6 x - y = 11$ (v) $(m^{2} - m n) y = (m n + n^{2}) x + n^{2}$ and $(m n + m^{2}) y = (m n + n^{2}) x + m^{3}$ .

Find the angle between each of the following pairs of straight lines: (i) 3x+y+12=0 and x+2y−1=0 (ii) 3x−y+5=0 and x−3y+1=0 (iii) 3x+4y−7=0 and 4x−3y+5=0 (iv) x−4y=3 and 6x−y=11 (v) (m2−mn)y=(mn+n2)x+n2 and (mn+m2)y=(mn+n2)x+m3.

Answer»

(i) $3 x + y + 12 = 0$ and $x + 2 y - 1 = 0$

(ii) $3 x - y + 5 = 0$ and $x - 3 y + 1 = 0$

(iii) $3 x + 4 y - 7 = 0$ and $4 x - 3 y + 5 = 0$

(iv) $x - 4 y = 3$ and $6 x - y = 11$

(v) $(m^{2} - m n) y = (m n + n^{2}) x + n^{2}$ and $(m n + m^{2}) y = (m n + n^{2}) x + m^{3}$ .