Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the equation of the plane passing through the point $(1,4,−2)$ and parallel to the plane $2x−y+3z+7=0$.

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The foot of the perpendicular from the point (1, 6, 3) to the line x1=y−12=z−23 is

Find the radius of the circular section of the sphere $∣r∣=5$ by the plane $ri^+2j^ −k^˙ =43 ˙$

What are the direction ratios of the line determined by the planes x−y+2z=1 andx+y−z=3?

Find the length of the perpendicular drawn from the point$(5,4,−1)$ to the line $r=i^+λ(2i^+9j^ +5k^),$ wher $λ$ is a parameter.

The Cartesian equation of a line is $2x−3 =−2y+1 =5z−3 $ . Find the vector equation of the line.

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

The direction ratios of the normal to the plane passing through the points (1, -2, 3), (-1, 2, -1) and parallel to x−22=y+13=z4 is

Find the shortest distance between the lines $r=(1−λ)i^+(λ−2)j^ +(3−2λ)k^andr=(μ+1)i^+(2μ+1)k^˙$