document.write( "Question 940706: Where does the line (x; y; z) = (4; 2; 1) + t(-2;-1; 0), (t is an element of the Real numbers), intersect the plane with general
\n" ); document.write( "equation 2x - y + 3z = 6?\r
\n" ); document.write( "\n" ); document.write( "any help would be appreciated cheers \n" ); document.write( "

Algebra.Com's Answer #573344 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
So the line is then,
\n" ); document.write( "( $\"4-2t\"$ , $\"2-t\"$ , $\"1%2B0t\"$ )=( $\"4-2t\"$ , $\"2-t\"$ , $\"1\"$ )
\n" ); document.write( "Substitute this into the plane equation and solve for $\"t\"$ .
\n" ); document.write( " $\"2x-y%2B3z=6\"$
\n" ); document.write( " $\"2%284-2t%29-%282-t%29%2B3%281%29=6\"$
\n" ); document.write( " $\"8-4t-2%2Bt%2B3=6\"$
\n" ); document.write( " $\"9-3t=6\"$
\n" ); document.write( " $\"-3t=-3\"$
\n" ); document.write( " $\"t=1\"$
\n" ); document.write( "So then,
\n" ); document.write( "( $\"4-2\"$ , $\"2-1\"$ , $\"1\"$ )=( $\"2\"$ , $\"1\"$ , $\"1\"$ ) is the intersection point. \n" ); document.write( "

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