document.write( "Question 1160838: Find an orthonormal basis of the plane x−4y−z=0.
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Algebra.Com's Answer #852182 by ikleyn(52793) $\"\"$ $\"About$

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document.write( "Consider two vectors  V1 = (1,0,1)  and V2 = (2,1,-2).\r\n" );
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document.write( "You can manually check that both vectors V1 and V2 satisfy the given equation - \r\n" );
document.write( "- so, they belong to the plane described by this equation.\r\n" );
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document.write( "Next, it is clear that vectors V1 and V2 are linearly independent - hence, they form \r\n" );
document.write( "a basis in the plane described by the given equation.\r\n" );
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document.write( "The fact is that vectors V1 and V2 are orthogonal.\r\n" );
document.write( "You may check it on your own.\r\n" );
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document.write( "To get vectors V1 and V2 orthonormal, we should divide each vector by its length.\r\n" );
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document.write( "Doing so, we get orthonormal vectors  ( ,,)  and  (,,).\r\n" );
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