Find the equation of the plane through the point `2veci+3vecj-veck` and perpendicular to the vector `3veci-4vecj+7veck`.

Find the equation of the plane through the point 2veci-vecj+veck and perpendiulr to the vector 4veci+2vecj-3veck . Determine the perpendicular distance of this plane from the origin.

Find the equation of the plane through the 2veci+3vecj-veck and perpendicular to the vector 3veci+2vecj-2vecj . Determine the perpendicular distance of this plane from the origin.

Find the equation of a plane passing throug the piont A(3,-2,1) and perpendicular to the vector 4veci+7vecj-4veck . If PM be perpendicular from the point P(1,2,-1) to this plane find its length.

Find the vector equation of the through the points 2veci+vecj-3veck and parallel to vector veci+2vecj+veck

Find the equation of a line through a point C of position vector vec c=3veci+2vecj and perpendicular to the vector vecb=veci-vecj in the xy-plane.

Find the equation of the plane through the origin and the points 4vecj and 2veci+veck. Find also the point in which this plane is cut by the line joining points veci-2vecj+veck and 3veck-2vecj .

Find the equation of the plane passing through three given points A(-2veci+6vecj-6veck),B(-3veci+10vecj-9veck) and C(-5veci+vec(6k))

A non zero vector veca is parallel to the line of intersection of the plane determined by the vectors veci,veci+vecj and the plane determined by the vectors veci-vecj, veci+veck find the angle between veca and the vector veci-2vecj+2veck .

Find the cosine of the angel between the planes vecr.(2veci-3vecj-6veck)=7 and vecr.(6veci+2vecj-9veck)=5

Find the direction cosines and unit vector along the vector vecr=2veci+vecj+3veck .