class 12

Math

3D Geometry

Three Dimensional Geometry

If the distance between the plane $Ax−2y+z=d.$ and the plane containing the lies $2x+1 =3y−2 =4z−3 and3x−2 =44−3 =5z−4 $ is $6 ,$ then $∣d∣$ is

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Find the equation of the plane passing thorugh the line of intersection of the planes $2x−y=0$ and $3z−y=0$, and perpendicular to the plane $4x+5y−3z=9$.

Find the vector equation of the plane passing through the intersection of the planes $r⋅(2i^−7j^ +4k^)=3$ and $r⋅(3i^−5j^ +4k^)+11=0$, and passing through the point $(−2,1,3)$.

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

Reduce the equation $2x−3y+5z+4=0$ to intercept form and find the intercepts made by it on the coordinate axes.

For the following planes, find the direction cosines of the normal to the plane and the distance of the plane from the origin.$z=3$.

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 $(2,1,0)$ from the plane $2x+y+2z+5=0$.

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 $r⋅(2i^−j^ +k^)+8=0$.