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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Find the equation of a plane passing through the points A(a,0,0),B(0,b,0) and C(0,0,c).
Find the coordinates of the foot of the perpendicular drawn from the origin to the plane 2x+3y+4z−12=0.
The distance between the parallel planes 2x−3y+6z=5 and 6x−9y+18z+20=0, is?
Find the equation of the plane passing through the point A(−1,−1,2) and perpendicular to each of the planes 3x+2y−3z=1 and 5x−4y+z=5.
A line makes angles 90o,135o and 45o with positive directions of x-axis, y-axis and z-axis respectively. What are the direction cosines of the line?
Find the distance between the parallel planes 2x+3y+4z=4 and 4x+6y+8z=12.
If (a1,b1,c1 and (a2,b2,c2) be the direction ratios of two parallel lines then
Find the vector equation of the line passing through the point with position vector (i^−2j^+5k^) and perpendicular to the plane r⋅(2i^−3j^−k^)=0.