Class 12

Math

3D Geometry

Three Dimensional Geometry

Find the vector equation of a plane whose Cartesian equation is $5x−7y+2z+4=0$.

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Find the vector equation of the following planes in Cartesian form: $r=i^−j^ +λ(i^+j^ +k^)+μ(i^−2j^ +3k^)˙$

Find the distance of the point $P(a,b,c)$ from the x-axis.

The angle between the line x−2a=y−2b=z−2c and the plane ax+by+cz+6=0 is

The direction consines of two lines are related byl+m+n=0al2+bm2+cn2=0. The lines are parallel if

Find the equation of the sphere described on the joint of points $AandB$ having position vectors $2i^+6j^ −7k^and−2i^+4j^ −3k^,$ respectively, as the diameter. Find the center and the radius of the sphere.

The shortest distance between the skew linesl1:r⃗ =a⃗ 1+λb⃗ 1l2:r⃗ =a⃗ 2+μb⃗ 2 is

If Q is the image of the point P(2, 3, 4) under the reflection in the plane x−2y+5z=6, then the equation of the line PQis

The plane $ax+by=0$ is rotated through an angle $α$ about its line of intersection with the plane $z=0.$ Show that he equation to the plane in the new position is $aby±za_{2}+b_{2} andα=0.$