class 12

Math

3D Geometry

Three Dimensional Geometry

The shortest distance between line $y-x=1$and curve $x=y_{2}$is :

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Prove that the normals to the planes $4x+11y+2z+3=0$ and $3x−2y+5z=8$ are perpendicular to each other.

Find the equation of the plane passing through the line of intersection of the planes $x+2y+3z−5=0$ and $3x−2y−z+1=0$ and cutting off equal intercepts on the x-axis and z-axis.

Find the direction cosines of the line $24−x =6y =31−z $.

Write the angle between the line $2x−1 =1y−2 =−2z+3 $ and the plane $x+y+4=0$.

Find the vector equation of the plane passing through the point $(3i^+4j^ +2k^)$ and parallel to the vectors $(i^+2j^ +3k^)$ and $(i^−j^ +k^)$.

What are the direction cosines of the y-axis?

Find the distance of the point $(2i^−j^ −4k^)$ from the plane $r⋅(3i^−4j^ +12k^)=9$.

The direction ratios of a line are $2,6,−9$. What are its direction cosines?