At what points does the line meet the co ordinate planes

At what point does r=(-4,6,-2) +t(2,-1,4) meet the coordinate planes?

L : (x,y,z) = (-4,6,-2) + t(2,-1,4)

∴ (x+4)/2 = (y-6)/(-1) = (z+2)/4 = t ...... (1)
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To find its intersection with xy-plane,

putting z = 0 in (1), we get :

... (x+4)/2 = (y-6)/(-1) = (0+2)/4 = 1/2

∴ (x+4)/2 = 1/2 ... and ... (y-6)/(-1) = 1/2

∴ x = -3 ... and ... y = 11/2

∴ line L meets xy-plane in ( -3, 11/2, 0 ) ............ Ans.(i)
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In a similar way, now you can find

its intersections with yz-plane(x=0)

and zx-plane(y=0).
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