Intersection of a line and plane

Consider a plane x+2y+3z=15 and a line (x-1)/(2)=(y+1)/(3)=(z-2)/(4) then find the distance of origin from point of intersection of line and plane.

Find the ratio in which the plane 2x-3y+z=8 divides the line segment joining the points A(3, -2,1) and B(1, 4, -3). Also find the point of intersection of the line and the plane.

The square of the distance of the point of intersection of the line and the plane (x-1)/(2)=(y-2)/(3)=(z+1)/(6) and the plane 2x-y+z=6 from the point (- 1, -1, 2) is_________

Find the ratio in which the plane x-2y+3z=5 divides the jion of A(3,-5,4) and B(2,3-7). Find the coordinats of the point intersection of the line and the plane.

A variable line passing through the point P(0, 0, 2) always makes angle 60^(@) with z-axis, intersects the plane x+y+z=1 . Find the locus of point of intersection of the line and the plane.

Find the equation of a line passing through the point (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.

A plane P passes through the line of intersection of the planes 2x-y+3z=2,x+y-z=1 and the point (1,0,1). What are the direction ratios of the line of intersection of the given planes ?

A plane P passes through the line of intersection of the planes 2x-y+3z=2.x+y-z=1 and the point (1,0,1) What are the direction ration of the line of intersection of the given planes

Equation of plane passing through intersection of two planes and perpendicular to a plane

A line L passes through the point P(5,-6,7) and is parallel to the planes x+y+z=1 and 2x-y-2z=3. What are the direction ratios of the line of intersection of the given planes?