Three Dimensional Geometry
Find the distance of the point A(−1,−5,−10) from the point of intersection of the line r=(2i^−j^+2k^)+λ(3i^+4j^+2k^) and the plane r⋅(i^−j^+k^)=5.
If the x-coordinate of a point P on the join of Q(22,1)andR(5,1,−2)is4, then find its z− coordinate.
Find the point of intersection of line passing through (0,0,1) and the intersection lines x+2u+z=1,−x+y−2zandx+y=2,x+z=2 with the xy plane.
The point P is the intersection of the straight line joining the points Q(2,3,5) and R(1,−1,4) with the plane 5x−4y−z=1. If S is the foot of the perpendicular drawn from the point T(2,1,4) to QR, then the length of the line segment PS is (A) 21 (B) 2 (C) 2 (D) 22
Equation of a line in the plane π=2x−y+z−4=0 which is perpendicular to the line l whose equation is 1x−2=−1y−2=−2z−3 and which passes through the point of intersection of l and π is (A) 1x−2=5y−1=−1z−1 (B) 3x−1=5y−3=−1z−5 (C) 2x+2=−1y+1=1z+1 (D) 2x−2=−1y−1=1z−1
A plane passes through a fixed point (a,b,c)˙ The locus of the foot of the perpendicular to it from the origin is a sphere of radius a. 21a2+b2+c2 b. a2+b2+c2 c. a2+b2+c2 d. 21(a2+b2+c2)
The projection of the line −1x+1=2y=3z−1 on the plane x−2y+z=6 is the line of intersection of this plane with the plane a. 2x+y+2=0 b. 3x+y−z=2 c. 2x−3y+8z=3 d. none of these