document.write( "Question 1104421: GIVEN 4 noncoplanar points, no three of which are collinear. How many planes are determined by the 4 points? Thanks! \n" ); document.write( "
Algebra.Com's Answer #719151 by jim_thompson5910(35256)![]() ![]() ![]() You can put this solution on YOUR website! \n" ); document.write( "Rule: Three noncollinear points are needed to uniquely define a plane\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Call the points A, B, C and D. There are exactly four ways to pick three points from this list where order doesn't matter. Put another way, there are 4 ways to exclude a point that isn't going to be determining a plane\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Those four ways are: \n" ); document.write( "{B, C, D} ... notice we leave out A \n" ); document.write( "{A, C, D} ... notice we leave out B \n" ); document.write( "{A, B, D} ... notice we leave out C \n" ); document.write( "{A, B, C} ... notice we leave out D\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Alternatively, you can use the n C r formula to get the same result. Use n = 4 and r = 3 \n" ); document.write( "n C r = (n!)/(r!(n-r)!) \n" ); document.write( "4 C 3 = (4!)/(3!*(4-3)!) \n" ); document.write( "4 C 3 = (4!)/(3!*1!) \n" ); document.write( "4 C 3 = (4*3!)/(3!*1!) \n" ); document.write( "4 C 3 = (4)/(1!) \n" ); document.write( "4 C 3 = (4)/(1) \n" ); document.write( "4 C 3 = 4\r \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Answer: 4 planes \n" ); document.write( " \n" ); document.write( " |