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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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 $90_{o},135_{o}$ and $45_{o}$ 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 $(a_{1},b_{1},c_{1}$ and $(a_{2},b_{2},c_{2})$ 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 $r⋅(2i^−3j^ −k^)=0$.