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

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 point 2veci+3vecj-veck and perpendicular to the vector 3veci-4vecj+7veck .

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

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

Find the set of vectors reciprocal to the set of vectors 2veci+3vecj-veck, veci-vecj-veck, -veci+2vecj+2veck

The torque about the point 3veci-vecj+3veck of a force 4veci+2vecj+veck through the point 5veci+2vecj+4veck is