Three Dimensional Geometry
Find the shortest distance between the lines r=(1−λ)i^+(λ−2)j^+(3−2λ)k^andr=(μ+1)i^+(2μ+1)k^˙
The equation of the plane which passes through the line of intersection of planes r⃗ .n⃗ 1=q1,r⃗ .n⃗ 2=q And is parallel to the line of intersection of planes r⃗ .n⃗ 3=q3 and r⃗ .n⃗ 4=q4is
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˙
The centre of the circle given by ri^+2j^+2k^˙=15and∣∣r−(j^+2k^)∣∣=4 is a. (0,1,2) b. (1,3,5) c. (−1,3,4) d. none of these
Line L1 is parallel to vector α=−3i^+2j^+4k^ and passes through a point A(7,6,2) and line L2 is parallel vector β=2i^+j^+3k^ and point B(5,3,4)˙ Now a line L3 parallel to a vector r=2i^−2j^−k^ intersects the lines L1andL2 at points CandD, respectively, then find ∣∣CD∣∣˙
Find the equation of the plane perpendicular to the line 2x−1=−1y−3=2z−4 and passing through the origin.
Find the length and the foot of the perpendicular from the point (7, 14, 5) to the plane 2x+4y−z=2. Also, the find image of the point P in the plane.