The condition of the lines `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+c c_1+1=0`
(C) `ac_1+b b\'+c c\'=0`
(D) `aa_1+c c_1-1=0`

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\'+c c' + 1=0 (B) aa\'+b b\'+c c'+1=0 (C) aa\'+b b\'+c c'=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 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

Find the condition for two lines a_(1)x+b_(1)y+c_(1)=0 and a_(2)x+b_(2)y+c_(2)=0 to be (i) parallel (ii) perpendicular

Prove that the line x=a y+b ,\ z=c y+d\ a n d\ x=a^(prime)y+b^(prime),\ z=c^(prime)y+d^(prime) are perpendicular if aa^(prime) + c c^(prime) + 1=0

The sum of the intercepts made by the plane a x+b y+c z=d on the three axes of reference is a+b+c (B) 1/a+1/b+1/c (C) d(1/a+1/b+1/c) (D) none of these

Direction ratios of two lines are a ,b ,c a n d1//b c ,1//c a ,1//a bdot Then the lines are ______.

If the origin lies in the acute angle between the lines a_1 x + b_1 y + c_1 = 0 and a_2 x + b_2 y + c_2 = 0 , then show that (a_1 a_2 + b_1 b_2) c_1 c_2 lt0 .

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_2y+c_2z+d_2=0

If the solution set of the inequaiton (x+4)(x-1)(x-3)(x+1)<0 is x in (a , b)uu(c , d) then (a) a+b+c+d=1 (b) a+b+c+d=2 (c) a b c d=12 (d) a b+c d=7