The condition of rthe ines `x=az+b,y=cz+d and x=a_1z+b_1,y=c_1z+d_1` to be perpendicular is (A) `ac_1+a_1c+1=0` (B) `aa_1+cc_1+1=0` (C) `ac_1+bb\'+cc\'=0` (D) `(aa_1+cc_1-1=0`

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

If the planes ax+by+cz+d=0anda_(1)x+b_(1)y+c_(1)z+d_(1)=0 be mutually perpendicular , then

the two lines x=ay+b,z=cy+d and x=a\'y+b,z=c\'y+d\' will be perpendicular, if and only if: (A) aa\'+cc\'=1=0 (B) aa\'+bb\'+cc\'=1=0 (C) aa\'+bb\'+cc\'=0 (D) (a+a\')+(b+b\')+(c+c\')=0

If the lines x=a_(1)y + b_(1), z=c_(1)y +d_(1) and x=a_(2)y +b_(2), z=c_(2)y + d_(2) are perpendicular, then

The equation of the plane passng throuogh (1,1,1) and (1,-1,-1) and perpendicular to 2x-y+z+5=0 is (A) 2x+5y+z-8=0 (B) x+y-z-1=0 (C) 2x+5y+z+4=0 (D) x-y+z-1=0

findthe equationof the plane passing through the point (alpha, beta, gamma) and perpendicular to the planes a_1x+b_1y+c_1z+d_1=0 and a_2x+b_2+yc_2z+d_2=0

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 one of the roots of equation ax^2+bx+c=0 may be reciprocal of one of the roots of a_1x^2+b_1x+c_1=0 if (aa_1-c c_1)^2=(bc_1-ab_1)(b_1c-a_1b)

The equation of the tangent to the curve y=sec x at the point (0,1) is (a) y=0 (b) x=0 (c) y=1 (d) x=1

The roots of the equation |[1,1,1],[a,x,a],[b,b,x]|=0 are (a) 1,1, (b) 1,a (c) 1,b, (d) a,b