How to find the point where the line x = –1 – t, y = 2 + t, z = 1+ t intersects the plane 3x + y + 3z = 1 ?

1 Answer
Alan P.
Dec 9, 2015

#(x,y,z) = (0,1,0)#

Explanation:

Given
[1]#color(white)("XXX")x=color(green)(-1-t)#
[2]#color(white)("XXX")y=color(red)(2+t)#
[3]#color(white)("XXX")z=color(blue)(1+t)#

[4]#color(white)("XXX")3x+y+3z=1#

Substitute the expressions for #x, y, z# from [1], [2], and [3] into [4]
[5]#color(white)("XXX")3(color(green)(-1-t))+color(red)(2+t)+3(color(blue)(1+t))=1#

Simplify [5]
[6]#color(white)("XXX")2+t=1#

[7]#color(white)("XXX")t=color(cyan)(-1)#

#(x,y,z) = (-1-(color(cyan)(-1)),2+color(cyan)(-1),1+color(cyan)(-1))#
#color(white)("XXXX")=(0,1,0)#

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