class 12

Math

3D Geometry

Three Dimensional Geometry

The distance of the point (1, 0, 2) from the point of intersection of the line $3x−2 =4y+1 =12z−2 $and the plane x y + z = 16, is :

Connecting you to a tutor in 60 seconds.

Get answers to your doubts.

Find the vector equation of a plane passing through the point $(1,2,3)$ and parallel to the lines whose direction ratios are $1,−1,−2$ and $−1,0,2$.

Find the acute angle between the following planes.$x+y−z=4$ and $x+2y+z=9$.

Find the distance between the planes $x+2y+3z+7=0$ and $2x+4y+6z+7=0$.

The equation of a plane which is perpendicular to $(2i^−3j^ +k^)$ and at a distance of $5$ units from the origin is?

Show that the line $r=(2i^+5j^ +7k^)+λ(i^+3j^ +4k^)$ is parallel to the plane $r⋅(i^+j^ −k^)=7$. Also, find the distance between them.

Find the angle between the line $2x+1 =3y =6z−3 $ and the plane $10x+2y−11z=3$.

Find the angle between the line $r=(2i^−j^ +3k^)+λ(3i^−j^ +2k^)$ and the plane $r⋅(i^+j^ +k^)=3$.

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 $(2i^−3j^ +4k^)$.