Prove that if the lines x = ay + b, z = cy + d and x = a'y + b', z = c'y + d' are perpendiclar to each other aa' + cc' + 1 = 0.

If the lines x = ay + b ,z = cy + d and x= a'z + b',y = c'z + d'' are perpendicular then ..........

The two lines x=ay+b, z=cy+d and x=a'y+b', z=c'y+d' are perpendicular to each other, if

Show that the lines (x-2)/(3)=(y+1)/(-2)=2 and (x-1)/(1)=(2y+3)/(3)=(z+5)/(2) are perpendiclar to each other.

Show that the lines (x-5)/(7)=(y+2)/(-5)=z/1 and x/1=y/2=z/3 are perpendicular to each other.

If the lines 2x-y+3z + 4 = 0=ax + y-z + 2 and x-3y + z=0 =x + 2y + z +1 are coplannar then the value of a is ...........

If the lines (2x-5)/(k) = (y+2)/(-5) = (z)/(1) and (x)/(1) = (y)/(2) = (z)/(3) are perpendicular to each other, then value of k is....................

Prove that the lines x=2 (y-1)/(3) = (z-2)/(1) and x = (y-1)/(1) = (z+1)/(3) are skew lines.

If x, y, z are not all zero & if ax + by + cz=0, bx+ cy + az=0 & cx + ay + bz = 0 , then prove that x: y : z = 1 : 1 : 1 OR 1 :omega:omega^2 OR 1:omega^2:omega , where omega is one ofthe complex cube root of unity.

In the following cases, find the coordinates of the foot of the perpendicular drawn from the origin : (a) 2x + 3y + 4z - 12 = 0 (b) 3y + 4z - 6 = 0 (c) x + y + z = 1 (d) 5y + 8 = 0

Statement 1 is True: Statement 2 is True; Statement 2 is a correct explanation for statement 1 Statement 1 is true, Statement 2 is true 2 Statement 2 not a correct explanation for statement 1. Statement 1 is true, statement 2 is false Statement 1 is false, statement 2 is true Statement I: If a ,\ \ b , c in R\ a n d a!=b!=c\ a n d\ x ,\ y ,\ z are non zero. Then the system of equations a x+b y+c z=0,b x+c y+a z=0,c x+a y+b z=0 has infinite solutions. because Statement II: If the homogeneous system of equations has non trivial solution, then it has infinitely many solutions. a. A b. \ B c. \ C d. D