document.write( "Question 1141441: Find the volume of the parallelepiped determined by the vectors →a=⟨5,3,−1⟩, →b=⟨0,4,2⟩, →c=⟨2,5,1⟩. \n" ); document.write( "
Algebra.Com's Answer #762080 by ikleyn(52781)\"\" \"About 
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document.write( "The volume of the given parallelepiped is equal to the absolute value of the determinant of the 3x3-matrix\r\n" );
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document.write( "    Volume = | det \"%28matrix%283%2C3%2C++5%2C+3%2C+-1%2C++0%2C+4%2C+2%2C++2%2C+5%2C+1%29%29\" |.\r\n" );
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document.write( "So, calculate the determinant first\r\n" );
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document.write( "    det \"%28matrix%283%2C3%2C++5%2C+3%2C+-1%2C++0%2C+4%2C+2%2C++2%2C+5%2C+1%29%29\" = 5*(4*1 - 5*2) - 3*(0*1 - 2*2) + (-1)*(0*5 - 2*4) = -10,\r\n" );
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document.write( "and then take its absolute value as the volume\r\n" );
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document.write( "    Volume = | -10 | = 10.      ANSWER\r\n" );
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