Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the distance between the parallel planes $x+2y−2z+4=0$ and $x+2y−2z−8=0$.

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What is the distance between the planesx−2y+z−1=0 and−3x+6y−3z+2=0?

A plane passes through a fixed point $(a,b,c)˙$ Show that the locus of the foot of the perpendicular to it from the origin is the sphere $x_{2}+y_{2}+z_{2}−ax−by−cz=0.$

Find the equation of a plane containing the line of intersection of the planes $x+y+z−6=0and2x+3y+4z+5=0$ passing through $(1,1,1)$ .

Find the coordinates of the foot of the perpendicular drawn from point $A(1,0,3)$ to the join of points $B(4,7,1)andC(3,5,3)˙$

The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is:

The locus of a point, such that the sum of the squares of its distances from the planes x+y+z=0,x−z=0 And x−2y+z=0is 9, is

Find the vector equation of a line passing through $3i^−5j^ +7k^$ and perpendicular to theplane $3x−4y+5z=8.$

A variable plane which remains at a constant distance 3p from the origin cut the coordinate axes at A, B and C. The locus of the centroid of triangle ABC is