Prove that for all values of `lambdaa n dmu` , the planes `(2x)/a+y/b+(2z)/c-1+lambda(x/a-(2y)/b-z/c-2)=0` and `(4x)/a+(3y)/b-5+mu((5y)/b-(4z)/c+3)=0` intersect on the same line.

The lines (x-1)/2=(y-2)/3=(z-3)/4 and (x-1)/3=(y-2)/4=(z-3)/5 are (A) parallel to x-axis (B) skew (C) intersecting (D) none of these

The system of linear equations x + y + z = 0 (2x)/(a) + (3y)/(b) + (4z)/(c ) = 0 (x)/(a) + (y)/(b) + (z)/(c ) = 0 has non trivia solution then

The lines (x-1)/(2)=(y-2)/(4)=(z-3)/(7) and (x-1)/(4)=(y-2)/(5)=(z-3)/(7) are (A) perpendicular (B) intersecting (C) skew (D) parallel

If theta is the angel between the planes 2x-y+z-1=0 and x-2y+z+2=0 then costheta= (A) 2/3 (B) 3/4 (C) 4/5 (D) 5/6

If (a)/(x-1) + (4b)/(y-2b) + (9c)/(z-3c)= 6-a find (ax)/(x-1) + (2y)/(y-2b) + (3z)/(z-3c) = ?

Are the planes x+y-2z+4=0 and 3x+3y-6z+5=0 intersecting

The equation of the plane which is equally inclined to the lines (x-1)/(2)=(y)/(-2)=(z+2)/(-1) and =(x+3)/(8)=(y-4)/(1)=(z)/(-4) and passing through the origin is/are a.14x-5y-7z=0 b.2x+7y-z=0 c.3x-4y-z=0 d.x+2y-5z=0

The value of lambda such that x+3y+lambda z=0,2x+4y-z=0,x+5y-2z=0 has a nontrivial solution is

A plane through the line (x-1)/1=(y+1)/(-2)=z/1 has the equation (A) x+y+z=0 (B) 3x+2y-z=1 (C) 4x+y-2z=3 (D) 3x+2y+z=0

The equation of the plane which passes through the point of intersection of lines (x-1)/(3)=(y-2)/(1)=(z-3)/(2), and (x-3)/(1)=(y-1)/(2)=(z-2)/(3) and at greatest distance from point (0,0,0) is a.4x+3y+5z=25 b.4x+3y=5z=50c3x+4y+5z=49d.x+7y-5z=2