Three Dimensional Geometry
For a>b>c>0, if the distance between (1,1) and the point of intersection of the line ax+by−c=0 is less than 22 then,
The equations of motion of a rocket are x=2t,y=−4tandz=4t, where timet is given in seconds, and the coordinates of a moving points in kilometers. What is the path of the rocket? At what distance will be the rocket from the starting point O(0,0,0) in 10s?
If the plane 2ax−3ay+4az+6=0 passes through the midpoint of the line joining the centres of the spheres x2+y2+z2+6x−8y−2z=13 and x2+y2+z2−10x+4y−2z=8 then a equals
The point of intersecting of the line passing through (0,0,1) and intersecting the lines x+2y+z=1,−x+y−2z=2andx+y=2,x+z=2 with xy-plane is
Given the line L:x−13=y+12=z−3−1 and the planeπ:x−2y=z. of the following assertions, the only one that is always true is
If r⃗ =(i^+2j^+3k^)+λ(i^+j^+k^) and r⃗ =(i^+2j^+3k^)+μ(i^+j^−k^) are two lines, then the equation of acute angle bisector of two lines is
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