The length of projection of the line segment joining the points `(1,0,-1)a n d(-1,2,2)` on the plane `x+3y-5z=6` is equal to a. `2` b. `sqrt((271)/(53))` c. `sqrt((472)/(31))` d. `sqrt((474)/(35))`

Find the equation of the plane through the points (2, 3,1)a n d(4,-5,3) and parallel to the x-axis.

The ration in which the line segement joining the points (4,-6) and (3,1) is divided by the parabola y^2=4x is (a) (-20+-sqrt(155))/(11):1 (b) (-20+-sqrt(155))/(11):2 (c) -20+-2sqrt(155): 11 (d) -20+-sqrt(155): 11

If tan^(-1)x+2cot^(-1)x=(2pi)/3, then x , is equal to (a) (sqrt(3)-1)/(sqrt(3)+1) (b) 3 (c) sqrt(3) (d) sqrt(2)

If the segments joining the points A(a , b)a n d\ B(c , d) subtends an angle theta at the origin, prove that : costheta=(a c+b d)/sqrt((a^2+b^2)(c^2+d^2))

Equation(s) of the straight line(s), inclined at 30^0 to the x-axis such that the length of its (each of their) line segment(s) between the coordinate axes is 10 units, is (are) (a) x+sqrt(3)y+5sqrt(3)=0 (b) x-sqrt(3)y+5sqrt(3)=0 (c) x+sqrt(3)y-5sqrt(3)=0 (d) x-sqrt(3)y-5sqrt(3)=0

Equation of the pane passing through the points (2,2,1)a n d(9,3,6),a n d_|_ to the plane 2x+6y+6z-1=0 is a. 3x+4y+5z=9 b. 3x+4y-5z=-9 c. 3x+4y-5z=9 d. none of these

Shortest distance between the lines (x-1)/1=(y-1)/1=(z-1)/1a n d(x-2)/1=(y-3)/1=(z-4)/1 is equal to a. sqrt(14) b. sqrt(7) c. sqrt(2) d. none of these

If x=1+1/(3+1/(2+1/(3+1/(2oo)))) a sqrt(5/2) b. sqrt(3/2) c. sqrt(7/3) d. sqrt(5/3)

If the line joining the points (0,3)a n d(5,-2) is a tangent to the curve y=C/(x+1) , then the value of c is 1 (b) -2 (c) 4 (d) none of these

Equation of the pane passing through the points (2,2,1)a n d(9,3,6),a n d_|_ to the plane 2x+6y+6z-1=0 is a. 3x+4y+5z=9 b. 3x+4y-5z=9 c. 3x+4y-5z=9 d. none of these