Find the vector equation of a line passing through the point with position vector `(2hati-3hatj-5hatk)` and perpendicular to the plane `vecr*(6hati-3hatj-5hatk)+2=0`. Also, find the point of intersection of this line and the plane.

Find the equation of the line passing through the point with position vector hati-hatj+2hatk and perpendicular to the plane vecr.(2hati-hatj+3hatk)=5 .

Find the vector equation of a plane passing through the point having position vector 2hati+hatj+hatk and perpendicular to the vector: 4hati-2hatj+3hatk .

Find the vector equation of the plane passing through three points with position vectors hati+hatj-2hatk, 2hati-hatj+hatk and hati+2hatj+hatk . Also find the co-ordinates of the point of intersection of this plane and the line vecr=3hati-hatj-hatk+lambda(2hati-2hatj+hatk) .

Find the vector equation of the line passing through the point (3,1,2) and perpendicular to the plane vecr*2hati-hatj+hatk)=4 . Also find the point of intersection of this line and the plane.

Find the vector equation of the line passing through the point (1,2,1) and perpendicular to the plane vecr.(2hati-hatj+hatk)=10 . Find the point of intersection of this line and the plane.

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 vector equation of a line passing through the point with position vector hati-2hatj-3hatk and parallel to the line joining the points with position vectors hati-hatj+4hatk and 2hati+hatj+2hatk . Also find the cartesian form of the equation.

Find the distance of the point whose position vector is 2hati+hatj-hatk from the plane vecr.(hati-2hatj+4hatk)=9 .

Find the vector equation of a line passing through a point with position vector 2hati-hatj+hatk and parallel t the line joining the points with position vectors -hati+4hatj+hatk and hati+2hatj+2hatk . Also, find the cartesian equivalent of the equation.

Find the vector equation of the line passing through (1, 2, 3) and perpendicular to the plane vecr cdot(hati+2hatj-5hatk) + 9 = 0