class 12

Math

3D Geometry

Three Dimensional Geometry

Let L be the line of intersection of the planes $2x+3y+z=1$ and $x+3y+2z=2$. If L makes an angles $α$with the positive x-axis, then cos$α$ equals

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The distance of point A (-2, 3, 1) from the line PQ through P (- 3, 5, 2), which makes equal angles with the axes is

A ray of light passing through the point $A(1,2,3)$ , strikews the plane $xy+z=12atB$ and on reflection passes through point $C(3,5,9)˙$ Find the coordinate so point $B˙$

If a plane meets the equations axes at $A,BandC$ such that the centroid of the triangle is $(1,2,4),$ then find the equation of the plane.

Find the equation of the plane passing through the points $(1,0,−1)and(3,2,2)$ and parallel to the line $x−1=21−y =3z−2 ˙$

What are the direction cosines of a line which is equally inclined to the positive directions of the axes?

Find the image of the line $9x−1 =−1y−2 =−3z+3 $ in the plane $3x−3y+10z−26=0.$

The equation of the plane which makes with co-ordinate axes, a triangle with its centroid (α,β,γ)is

What is the angle between the planes2x−y+z=6 andx+y+2z=3?