class 12

Math

3D Geometry

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,

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The equations of motion of a rocket are $x=2t,y=−4tandz=4t,$ where time$t$ 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

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Find the image of the point $(1,2,3)$ in the line $3x−6 =2y−7 =−2z−7 $.

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If the direction consines of a line are (1c,1c,1c) then