document.write( "Question 1011207: Find a vector perpendicular to the given vector 2i+9j-6k
\n" ); document.write( "Please Show all your work step by step. \n" ); document.write( "
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\n" ); document.write( "Question:
\n" ); document.write( "Find a vector perpendicular to the given vector 2i+9j-6k
\n" ); document.write( "Please Show all your work step by step.
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\n" ); document.write( "Solution:
\n" ); document.write( "A vector will be denoted where x,y,z are the respective components.
\n" ); document.write( "We're looking for a vector perpendicular to P=<2,9,-6>.
\n" ); document.write( "In fact, there is an infinite number of vectors perpendicular to P.
\n" ); document.write( "We know that the cross product of two non-parallel vectors P, Q is perpendicular to both P and Q.
\n" ); document.write( "So by finding the cross product P and an arbitrary vector Q=, we can obtain the vector R=PxQ such that R is perpendicular to both P and Q, with the restriction that Q is not parallel to P, or Q does not equal kQ where k is a real number.
\n" ); document.write( "The cross product can be obtained by evaluation of the determinant
\n" ); document.write( "|i j k |
\n" ); document.write( "|2 9 -6|
\n" ); document.write( "|a b c |
\n" ); document.write( "which gives R=<9c+6b, -2c-6a, 2b-9a>
\n" ); document.write( "Thus
\n" ); document.write( "R=<9c+6b, -2c-6a, 2b-9a> is a vector perpendicular to P=<2,9,-6> for any vector Q= such that Q≠kP and k is a real number. \n" ); document.write( "
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