Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the angle between the lines whose direction ratios are:$1,1,2$ and $(3 −1),(−3 −1),4$

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Find the equation of a plane passing through the point $(2,−1,5)$, perpendicular to the plane $x+2y−3z=7$ and parallel to the line $3x+5 =−1y+1 =1z−2 $.

Show that the planes $2x−y+6z=5$ and $5x−2.5y+15z=12$ are parallel.

Find the equation of the plane parallel to the plane $2x−3y+5z+7=0$ and passing through the point $(3,4,−1)$. Also, find the distance between the two planes.

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 $r⋅(2i^−j^ +k^)+8=0$.

The vector equation of the x-axis is given by

If the lines $−3x−1 =2ky−2 =2z−3 $ and $3kx−1 =1y−1 =−5z−6 $ are perpendicular to each other then $k=$?

Find the vector and Cartesian forms of the equations of the plane containing the two lines $r=(i^+2j^ −4k^)+λ(2i^+3j^ +6k^)$ and $r=(3i^+3j^ −5k^)+μ(−2i^+3j^ +8k^)$.

Show that the four points $A(0,−1,0),B(2,1,−1),C(1,1,1)$ and $D(3,3,0)$ are coplanar. Find the equation of the plane containing them.