class 12

Math

3D Geometry

Three Dimensional Geometry

An equation of a plane parallel to the plane $x2y+2z5=0$and at a unit distance from the origin is

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Find the length and the foot of perpendicular drawn from the point $(2,3,7)$ to the plane $3x−y−z=7$.

Find the acute angle between the following planes.$r⋅(2i^−3j^ +4k^)=1$ and $r⋅(−i^+j^ )=4$.

If the equations of a line are $−33−x =−2y+2 =6z+2 $, find the direction cosines of a line parallel to the given line.

Find the distance of the point $(0,−3,2)$ from the plane $x+2y−z=1$, measure parallel to the line $3x+1 =2y+1 =3z $.

Find the vector and Cartesian equations of a plane which is at a distance of $29 6 $ from the origin and whose normal vector from the origin is $(2i^−3j^ +4k^)$.

Find the equation of the plane through the line of intersection of the planes $r⋅(2i^−3j^ +4k^)=1$ and $r⋅(i^−j^ )+4=0$ and perpendicular to the plane $r⋅(2i^−j^ +k^)+8=0$.

If a line makes angles $α,β$ and $γ$ with the x-axis, y-axis and z-axis respectively then $(sin_{2}α+sin_{2}β+sin_{2}γ )=$

What are the direction cosines of the y-axis?