Find a unit vector normal to the plane : `vecr*(2hati-3hatj+6hatk)+14=0`.

Find the unit vector perpendicular to the plane vecr.(6hati+3hatj-2hatk)+1=0 passing through the origin and directed from origin to the plane.

Find the direction cosines of the unit vector perpendicular to the plane vecr cdot(6hati-3hatj-2hatk) +1 = 0 passing through the origin.

Find a unit vector parallel to the sum of the vectors hati+hatj+hatk and 2hati-3hatj+5hatk .

Find the direction cosines of the perpendicular from the origin to the plane vecr.(2hati+2hatj-6hatk)+1=0 .

Find the vector equation of the plane passing through the intersection of the planes : vecr*(2hati-hatj+2hatk)=2 and vecr*(3hati+hatj-2hatk)=-2 and perpendicular to the veca=5hati-2hatj+3hatk .

Find the vector equation of the line through the origin, which is perpendicular to the plane vecr*(hati-2hatj+hatk)=3 .

Find the vector equation of the line passing through (1, 2, 3) and parallel to each of the planes vecr = (hati-hatj+2 hatk)= 5" and "vecr *(3hati- hatj+hatk)= 6 . Also find the point of intersection of the line thus obtained with the plane vecr * (2hati-hatj+hatk)= 4 .

Find the unit vector in the direction of the vector : veca =2hati-3hatj+6hatk .