document.write( "Question 1134088: line L1 and L2 has equation (x-3)/2 = (y-4)/-1 = (z+1)/1 and (x-5)/4 = (y-1)/3 = (z-1)/2. find Cartesian equation of the plane P which contain L1 and parallel to L2. L3 pass through point A(-3,-2,-1) and meets P at B(-1,2,1). find Cartesian equation of L3 and acute angle between P and L3 (in nearest degree). Another line L4 with Cartesian equation (x-2)/1 = (y+3)/2 = (z+2)/1 pass through plane P. find intersection point. \n" ); document.write( "
Algebra.Com's Answer #751736 by Edwin McCravy(20055)\"\" \"About 
You can put this solution on YOUR website!
L1: \"%28x-3%29%2F2+=+%28y-4%29%2F%28-1%29+=+%28z%2B1%29%2F1\"
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\n" ); document.write( "\n" ); document.write( "L1 is parallel to the vector < 2,-1,1 > and passes thru (3,4,-1)
\n" ); document.write( "L2 is parallel to the vector < 4,3,2 > and passes thru (5,1,1)\r
\n" ); document.write( "\n" ); document.write( "find Cartesian equation of the plane P which contain L1 and parallel to L2.
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document.write( "A vector perpendicular to both those lines will be perpendicular (normal) to the\r\n" );
document.write( "desired plane.\r\n" );
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document.write( "So we find a vector perpendicular to both vectors by crossing them:\r\n" );
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document.write( "< 2,-1,1 > × < 4,3,2 > =\r\n" );
document.write( " = \r\n" );
document.write( "< -5,0,10 >\r\n" );
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document.write( "So we want a plane containing the point (5,1,1) and having normal vector\r\n" );
document.write( "< -5,0,10 >, which is\r\n" );
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document.write( "-5(x - 5)+0(y - 1)+10(z - 1) = 0\r\n" );
document.write( "-5x + 25 + 10z - 10 = 0\r\n" );
document.write( "-5x + 10z + 15 = 0\r\n" );
document.write( "Divide through by -5\r\n" );
document.write( "x - 2z - 3 = 0\r\n" );
document.write( "x - 2z = 3\r\n" );
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document.write( "---------------------------------\r\n" );
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document.write( "L3 pass through point A(-3,-2,-1) and meets P at B(-1,2,1). \r\n" );
document.write( "Find Cartesian equation of L3 \r\n" );
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document.write( "-----------------------\r\n" );
document.write( "I have to stop here because something is wrong because B(-1,2,1) is not\r\n" );
document.write( "on plane P because substituting B(-1,2,1) into\r\n" );
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document.write( "     x - 2z = 3\r\n" );
document.write( "(-1) - 2(1) = 3\r\n" );
document.write( "       -1-2 = 3 \r\n" );
document.write( "         -3 = 3 is false. \r\n" );
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document.write( "Could it be that B(-1,2,1) could have supposed to have been B(1,2,-1)?\r\n" );
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document.write( "Check everything again.  If you answer below, I'll get back to you \r\n" );
document.write( "by email.\r\n" );
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document.write( "Edwin
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