Foot of perpendicular drawn from the origin to the plane ( 2 x-3 y+4 z=29 ) is

Step-by-step solution

Given equation of plane [ 2 x-3 y+4 z=29 (1) ] Normal vector of this plane is given by [ N =2 i -3 j +4 k ] Now, equation of line which passes through the origin and has the same direction as normal vectors ( N ) is [ array l x 2 = y -3 = z 4 = (2) x=2-x, y=-3 , z=4 (3) array ] The coordinates of the foot of the perpendicular is [ array l 4 +9 +16 =29 29 =29 =1 array ] Putting the value of ( ) in Eq. (3), we have ( x=2, y=-3, z=4 ) or ( (2,-3,4) )