[" If "(x-1)/(1)=(y-2)/(m)=(z+1)/(n)" is the equation of the line throueh "(1,2,-1)" and "(-1,0,1)" .then "(l,m,n)" s "],[[" (A) "(-1,0,1)," (B) "(1,1,-1)," (C) "(1,2,-1)," (D) "(0,1,0)]]

If (x-1)/(l)=(y-2)/(m)=(z+1)/(n) is the equation of the line through (1,2,-1) and (-1,0,1) then (l,m,n)

If (x-1)/l=(y-2)/m=(z+1)/n is the equation of the line through (1,2,-1) and (-1,0,1) , then (l,m,n)

The condition that the line (x-x_(1))/(l)=(y-y_(1))/(m)=(z-z_(1))/(n) lies in the plane ax+by+cz+d=0 is

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

If L(m,n)=int_(0)^(1)t^(m)(1+t)^(n),dt , then prove that L(m,n)=(2^(n))/(m+1)-n/(m+1)L(m+1,n-1)

The condition that the line (x-x_1)/l=(y-y_1)/m=(z-z_1)/n lies in the plane ax+by+cz+d=0 is

Show that if the axes are rectangular,the equation of the line through the point (x_(1),y_(1),z_(1)) at right angle to the lines (x)/(l_(1))=(y)/(m_(1))=(z)/(n_(1));(x)/(l_(2))=(y)/(m_(2))=(z)/(n_(2)) is (x-x_(1))/(m_(1)n_(2)-m_(2)n_(1))=(y-y_(1))/(n_(1)l_(2)-n_(2)l_(1))=(z-z_(1))/(l_(1)m_(2)-l_(2)m_(1))

Acute angle between the lines (x-1)/(l)=(y+1)/(m)=(z)/(n) and (x+1)/(m)=(y-3)/(n)=(z-1)/(l) where l>m>n and l,m,n are the roots of the cubic equation x^(3)+x^(2)-4x=4 is equal to: cos^(-1)(4)/(9)(b)sin^(-1)(sqrt(65))/(9)2cos^(-1)sqrt((13)/(18))(d)cot^(-1)(4)/(65)