tan theta=|(m_(2)-m_(1))/(1+m_(1)m_(2))

If theta is the acute angle between the lines with slopes m1 and m2 then tan theta=(m_(1)-m_(2))/(1+m_(1)m_(2)) 2) if p is the length the perpendicular from point P(x1,y1) to the line ax +by+c=0 then p=(ax_(1)+by_(1)+c)/(sqrt(a^(2)+b^(2)))

A : If the angle between the lines kx-y+6=0, 3x+5y+7=0 is pi//4 one value of k is 4 R : If theta is angle between the lines with slopes m_(1), m_(2) then tan theta=(|m_(1)-m_(2)|)/(|1+m_(1)m_(2)|) .

If the loss in graviational potential energy to falling the sphere by h height and heat loss to surrounding at constant rate H are also taken to account the energy equation will modify to (A) m_(1) s_(1) (theta_(1)-theta) + (m_(1)gh)/(J) = m_(2) s_(2) (theta - theta_(2)) + m_(3) s_(3) (theta - theta_(2)) - H t (B) m_(1)s_(1) (theta_(1) -theta) - (m_(1)gh)/(J) = m_(2)s_(2)(theta -theta_(2)) + m_(3) s_(3) (theta -theta_(2)) + Ht (C) m_(1)s_(1) (theta_(1) -theta) + (m_(1)gh)/(J) = m_(2) s_(2) (theta - theta_(2)) + m_(3) s_(3) (theta -theta_(2)) + Ht (D) m_(1) s_(1) (theta_(1)-theta)-(m_(1)gh)/(J)=m_(2)s_(2)(theta-theta_(2)) +m_(3)s_(3)(theta-theta_(2))-Ht .

The lines y=m_(1)x,y=m_(2)xandy=m_(3)x make equal intercepts on the line x+y=1 Then (a) 2(1+m_(1))(1+m_(3))=(1+m_(2))(2+m_(1)+m_(3))(1+m_(1))(1+m_(3))=(1+m_(2))(1+m_(1)+m_(3))(1+m_(1))(1+m_(2))=(1+m_(3))(2+m_(1)+m_(3))(1+m_(1))(1+m_(3))=(1+m_(2))(1+m_(1)+m_(3))2(1+m_(1))(1+m_(3))=(1+m_(2))(1+m_(1)+m_(3))

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is

If the direction cosines of two lines are (l_(1), m_(1), n_(1)) and (l_(2), m_(2), n_(2)) and the angle between them is theta then l_(1)^(2)+m_(1)^(2)+n_(1)^(2)=1=l_(2)^(2)+m_(2)^(2)+n_(2)^(2) and costheta = l_(1)l_(2)+m_(1)m_(2)+n_(1)n_(2) If the angle between the lines is 60^(@) then the value of l_(1)(l_(1)+l_(2))+m_(1)(m_(1)+m_(2))+n_(1)(n_(1)+n_(2)) is