Three Dimensional Geometry
Find the distance of the point (2,1,0) from the plane 2x+y+2z+5=0.
Find the equation of the plane passing through (3,4,−1), which is parallel to the plane r2i^−3j^+5k^˙+7=0.
Find the equation of a line which passes through the point (1,1,1) and intersects the lines 2x−1=3y−2=4z−3and1x+2=2y−3=4z+1˙
Given α=3i^+j^+2k^andβ=i^−2j^−4k^ are the position vectors of the points AandB Then the distance of the point i^+j^+k^ from the plane passing through B and perpendicular to AB is (a) 5 (b) 10 (c)15 (d) 20
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
Find the equation of the plane which is parallel to the lines r=i^+j^+λ(2i^+j^+4k^)and−3x+1=2y−3=1z+2 and is passing through the point (0,1,−1 ).
The lines 1x−2=1y−3=−kz−4andkx−1=2y−4=1z−5 are coplanar if a. k=1or−1 b. k=0or−3 c. k=3or−3 d. k=0or−1