Find the distance of the point (1,2,0) from the point where the line joining A(2,-3,1) and B(3,-4,5) into the plane 2x+y+z=7?

equation of the line joining the points A(2,-3,1) and B(3,-4,5) is

suppose the line cuts the plane 2x+y+z=7 at point A (r+2, -r-3, 4r+1)

therefore

2(r+2)+(-r-3)+(4r+1)=7

2r+4-r-3+4r+1=7

5r=5

r=5/5=1

thus the coordinates of A is (1+2,-1-3,4+1) i.e. A(3, -4, 5)

therefore the required distance

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