document.write( "Question 942470: Find the angle between the planes 3x-y+z-5=0 and x+2y+2z+2=0. \n" ); document.write( "

Algebra.Com's Answer #574554 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
Find the normal of each plane, then use the dot product.
\n" ); document.write( " $\"N%5B1%5D\"$ =( $\"3\"$ , $\"-1\"$ , $\"1\"$ )
\n" ); document.write( " $\"N%5B2%5D\"$ =( $\"1\"$ , $\"2\"$ , $\"2\"$ )
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\n" ); document.write( " $\"N%5B1%5D%2AN%5B2%5D=abs%28N%5B1%5D%29abs%28N%5B2%5D%29cos%28theta%29\"$
\n" ); document.write( " $\"abs%28N%5B1%5D%29=sqrt%283%5E2%2B%28-1%29%5E2%2B1%5E2%29=sqrt%289%2B1%2B1%29=sqrt%2811%29\"$
\n" ); document.write( " $\"abs%28N%5B2%5D%29=sqrt%281%5E2%2B2%5E2%2B2%5E2%29=sqrt%281%2B4%2B4%29=sqrt%289%29=3\"$
\n" ); document.write( " $\"N%5B1%5D%2AN%5B2%5D=3%281%29%2B%28-1%29%282%29%2B1%282%29=3-2%2B2=3\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"3=sqrt%2811%29%2A3%2Acos%28theta%29\"$
\n" ); document.write( " $\"cos%28theta%29=1%2Fsqrt%2811%29\"$
\n" ); document.write( " $\"theta=72.5\"$ $\"degrees\"$ \n" ); document.write( "

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