Find the acute angle between the lines `(x-1)/l=(y+1)/m=1/na n d=(x+1)/m=(y-3)/n=(z-1)/lw h e r el > m > n ,a n dl ,m ,n` are the roots of the cubic equation `x^3+x^2-4x=4.`

Find the angle between the following pairs of line: (x+4)/3=(y-1)/5=(z+3)/4a n d(x+1)/1=(y-4)/1=(z-5)/2

Find the angle between the following pairs of line: (x-1)/2=(y-2)/3=(z-3)/(-3)a n d(x+3)/(-1)=(y-5)/8=(z-1)/4

Find the angle between the plane: 2x-3y+4z=1\ a n d-x+y=4.

Find the angle between the following pairs of line: (x-5)/1=(2y+6)/(-2)=(z-3)/1a n d(x-2)/3=(y+1)/4=(z-6)/5

Find the angle between the following pairs of line: (-x+2)/(-2)=(y-1)/7=(z+3)/(-3)a n d(x+2)/(-1)=(2y-8)/4=(z-5)/4

Distance of the point P(x_2, y_2, z_2) from the line (x-x_1)/l=(y-y_1)/m=(z-z_1)/n , where l,m,n are the direction cosines of the line, is

Find the equation of the plane through the line (x-x_1)/l_1=(y-y_1)/m_1=(z-z_1)/n_1 and parallel to the line (x-alpha)/l_2=(y-beta)/m_2=(z-gamma)/n_2

The equation of the plane containing the line (x-x_1)/l=(y-y_1)/m=(z-z_1)/n is a(x-x_1)+b(y-y_1)+c(z-z_1)=0,"" where (A) a x_1+b y_1+c z_1=0 (B) a l+b m+c n=0 (C) a/l=b/m=c/n (D) l x_1+m y_1+n z_1=0

If l : m = 2 (1)/(2) : 1(2)/(3) and m : n = 1 (1)/(4) : 3 (1)/(2) , find l : m : n

Find the conditions that the straight lines y=m_1x+c_1, y=m_2x+c_2a n d\ y=m_3x+c_3 may meet in a point.