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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For the following planes, find the direction cosines of the normal to the plane and the distance of the plane from the origin.$2x+3y−z=5$.

Find the vector equation of a line passing through the point $(1,2,3)$ and parallel to the vector $(3i^+2j^ −2k^ )$

Find the equation of the plane passing through the intersection of the planes $4x−y+z=10$ and $x+y−z=4$ and parallel to the line with direction ratios $2,1,1$. Find also the perpendicular distance of $(1,1,1)$ from this plane.

Find the value of $λ$ for which the line $2x−1 =3y−1 =λz−1 $ is parallel to the plane $r⋅(2i^+3j^ +4k^)=4$.

Find the equation of the plane which contains two parallel lines given by $1x−3 =−4y+2 =5z $ and $1x−4 =−4y−3 =5z−2 $.

Find the equation of the plane passing through the origin and perpendicular to each of the planes $x+2y−z=1$ and $3x−4y+z=5$.

Find the equation of the plane passing through the origin and parallel to the plane $5x−3y+7z+13=0$.

Find the equation of the plane passing through the intresection of the planes $x−2y+z=1$ and $2x+y+z=8$ and parallel to the line with direction ratio proportional to $1,2,1,$ find also the perpendicular distance of $(1,1,1)$ from this plane.