Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the distance of the point P(6,5,9) from the plane determined by the points $A(3,−1,2),B(5,2,4)$and $C(−1,−1,6)˙$

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Find the equation of the plane that contains the point $A(1,−1,2)$ and is perpendicular to both the planes $2x+3y−2z=5$ and $x+2y−3z=8$. Hence, find the distance of the point $P(−2,5,5)$ from the plane obtained above.

Find the vector and Cartesian equations of the plane passing through the point $(3,−1,2)$ and parallel to the lines $r=(−j^ +3k^)+λ(2i^−5j^ −k^)$ and $r=(i^−3j^ +k^)+μ(−5i^+4j^ )$.

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.

Find the angle between the line $r=(3i^+k^)+λ(j^ +k^)$ and the plane $r⋅(2i^−j^ +2k^)=1$.

Find the equation of the plane passing through group of points.$A(0,−1,−1),B(4,5,1)$ and $C(3,9,4)$.

Find the distance between the parallel planes $x+2y−2z+4=0$ and $x+2y−2z−8=0$.

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

Find the equation of the plane through the line of intersection of the planes $x−3y+z+6=0$ and $x+2y+3z+5=0$, and passing through the origin.