Three Dimensional Geometry
Find the length and the foot of the perpendicular drawn from the point (1,1,2) to the plane r⋅(2i^−2j^+4k^)+5=0.
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
Shortest distance between the lines 1x−1=1y−1=1z−1and1x−2=1y−3=1z−4 is equal to a. 14 b. 7 c. 2 d. none of these
Find the equation of the plane passing through A(2,2,−1),B(3,4, 2)andC(7,0,6)˙ Also find a unit vector perpendicular to this plane.
If the distance of the point P(1,−2,1) from the plane x+2y−2z=α,whereα>0,is5, then the foot of the perpendicular from P to the place is a. (38,34,−37) b. (34,−34,31) c. (31,32,310) d. (32,−31,−35)
Let A(1,1,1),B(2,3,5)andC(−1,0,2) be three points, then equation of a plane parallel to the plane ABC which is at distance 2 is a. 2x−3y+z+214=0 b. 2x−3y+z−14=0 c. 2x−3y+z+2=0 d. 2x−3y+z−2=0
A parallelepiped is formed by planes drawn through the points P(6,8,10)and(3,4,8) parallel to the coordinate planes. Find the length of edges and diagonal of the parallelepiped.