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

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 point 2hati+3hatj-hatk and perpendicular to vector 3hati+3hatj+7hatk. Determine the perpendicular distance of this plane from the origin.

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

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 the plane passing through the point (-1,2,1) and perpendicular to the line joining the points (-3,1,2)a n d(2,3,4)dot Find also the perpendicular distance of the origin from this plane.

Find the equation of the plane passing through the point (1,2,1) and perpendicular to the line joining the points (1,4,2)a n d(2,3,5)dot find also the perpendicular distance of the origin from this plane.

Find the vector equation of the line passing through the point (1,-1,2) and perpendicular to the plane 2 x-y+3z-5=0.

Find the vector equation of the line through the origin which is perpendicular to the plane vec rdot(( hat i+2 hat j+3 hat k)=3.

Find the vector equation of the plane through the points (2, 1, -1) and (-1, 3, 4) and perpendicular to the plane x-y+4z=10.