If the lines mx - ny + 5 = 0 and 2x + 3y + 6 = 0 are perpendicular to each other, then find the relation between m and n
mx−ny+5=0⇒mx+5=ny⇒ny=mx+5⇒y=mnx+5n∴Slope of line=mn⇒m1=mn∣∣
∣∣2x+3y+6=0⇒3y=−2x−6⇒y=−23x−2∴Slope of line=−23⇒m2=−23 ∵ Lines are perpendicular m1m2=−1 ⇒mn×(−23)=−1 ⇒2m=3n
(i) Lines 2x - by + 5 = 0 and ax + 3y = 2 are parallel to each other. Find the relation connecting a and b.
(ii) Lines mx + 3y + 7 = 0 and 5x - ny - 3 = 0 are perpendicular to each other. Find the relation connecting m and n.
Find the value of p if the lines, whose equations are 2x - y + 5 = 0 and px + 3y = 4 are perpendicular to each other.
If the lines lx+my+n=0, mx+ny+l=0 and nx+ly+m=0 are concurrent then (l,m,n≠0)