Three Dimensional Geometry
Find the acute angle between the following planes.
2x−y+z=5 and x+y+2z=7.
A line passes through the points (6,−7,−1)and(2,−3,1)˙ Find te direction cosines off the line if the line makes an acute angle with the positive direction of the x-axis.
A mirror and a source of light are situated at the origin 0 and at a point on OX respectively. A ray of light from the source strikes the mirror and is reflected. If the direction ratios of the normal to the plane are 1, -1, 1, then direction consines of the reflected rays are
A variable plane passes through a fixed point (a,b,c) and cuts the coordinate axes at points A,B,andC˙ Show that eh locus of the centre of the sphere OABCisxa+yb+zc=2.
Find the equation of the plane passing through A(2,2,−1),B(3,4, 2)andC(7,0,6)˙ Also find a unit vector perpendicular to this plane.