EXERCISE 6.6

EXERCISE . . Find the vector equation of a plane which is at a distance of units from the origin having , , as direction ratios of a normal to it. . Find the direction cosines of the normal to the plane . Also, find the non-parametric form of vector equation of a plane and the length of the perpendicular to the plane from the origin. . Find the vector and Cartesian equations of the plane passing through the point with position vector and normal to the vector . A plane passes through the point ( , , ) and the normal to the plane of magnitude makes equal acute angles with the coordinate axes. Find the equation of the plane. . Find the intercepts cut off by the plane ( ) on the coordinate axes. . If a plane meets the coordinate axes at , , A B C such that the centriod of the triangle ABC is the point ( , , ) u v w , find the equation of the plane. Vector - -